aa r X i v : . [ s t a t . O T ] N ov Statistical Science (cid:13)
Institute of Mathematical Statistics, 2010
A Conversation with James Hannan
Dennis Gilliland and R. V. Ramamoorthi
Abstract.
Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeatedgames was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II,Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play thatapply to selecting the best forecaster.James Hannan was born in Holyoke, Massachusetts on September 14, 1922. He attended St. Jerome’s High School and inJanuary 1943 received the Ph.B. from St. Michael’s College in Colchester, Vermont. Jim enlisted in the US Army Air Forceto train and serve as a meteorologist. This took him to army airbases in China by the close of the war. Following dischargefrom the army, Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To prepare for doctoralwork in statistics at the University of North Carolina that fall, Jim went to the University of Michigan in the summer of1947. The routine admissions’ physical revealed a spot on the lung and the possibility of tuberculosis. This caused Jim tostay at Ann Arbor through the fall of 1947 and then at a Veterans Administration Hospital in Framingham, Massachusettsto have his condition followed more closely. He was discharged from the hospital in the spring and started his study atChapel Hill in the fall of 1948. There he began research in compound decision theory under Herbert Robbins. Feeling theneed for teaching experience, Jim left Chapel Hill after two years and short of thesis to take a three year appointmentas an instructor at Catholic University in Washington, DC. When told that renewal was not coming, Jim felt pressure tofinish his degree. His 1953 UNC thesis contains results in compound decision theory, a density central limit theorem for thegeneralized binomial and exact and asymptotic distributions associated with a Kolmogorov statistic. He was encouraged toapply to the Department of Mathematics at Michigan State University and came as assistant professor in the fall of 1953.In the next few years, he accomplished his work on repeated games. The significance of the work was rediscovered by theon-line learning communities in computer science in the 1990s and the term
Hannan consistency was coined. His retirementcame in 2002 after a long career that included major contributions to compound and empirical Bayes decision theory andother areas. He and his colleague V´aclav Fabian co-authored
Introduction to Probability and Mathematical Statistics (Wiley1985).A
Hannan strategy is a strategy for the repeated play of a game that at each stage i plays a smoothed version of acomponent Bayes rule versus the empirical distribution Gi-1 of opponent’s past plays. [Play against the unsmoothed versionis often called (one-sided) fictitious play .] As in compound decision theory, performance is measured in terms of modifiedregret , that is, excess of average risk across stages i = 1 , . . . , n over the component game Bayes envelope R evaluated atGn. Hannan, James F., Approximation to Bayes Risk in Repeated Play, Contributions to the Theory of Games Hannan consistent strategy is one wherelimsup (modified regret) is not greater than zero. In the 1990s, greater recognition of Hannan’s work began to emerge; theterm Hannan consistency may have first appeared in Hart and Mas-Colell [
J. Econom. Theory (2001) 26–54].Early on, only his students and a few others were aware of the specifics of his findings. The failure of others to recognizethe specific results in the 1957 paper may be due to the cryptic writing style and notation of the author. The strategy forselecting forecasters in Foster and Vohra [8] [ Operations Research (1993) 704–709] is an unrecognized Hannan-strategy asis the strategy in Feder et al. [7] [ IEEE Trans. Inform. Theory (1992) 1258–1270]. Gina Kolata’s New York Times article,“Pity the Scientist who Discovers the Discovered” (February 5, 2006) uses the original Hannan discoveries as an example,although referring to him as a “statistician named James Hanna.”In May 1998, the Department of Statistics and Probability hosted a
Research Meeting in Mathematical Statistics in Honorof Professor James Hannan . Many came to honor Jim; the speakers included V´aclav Fabian, Stephen Vardeman, SumanMajumdar, Richard Dudley, Yoav Freund, Dean Foster, Rafail Khasminskii, Herman Chernoff, Michael Woodroofe, SomnathDatta, Anton Schick and Valentin Petrov.Jim was ever generous in giving help to students. He enjoyed improving results and was very reluctant to submit researchresults until much effort was made to improve them. Jim directed or co-directed the doctoral research of twenty students:William Harkness (1958), Shashikala Sukatme (1960), John Van Ryzin (1964), Dennis Gilliland (1966), David Macky (1966),Richard Fox (1968), Allen Oaten (1969), Jin Huang (1970), Vyagherswarudu Susarla (1970), Benito Yu (1971), RadheySingh (1974), Yoshiko Nogami (1975), Stephen Vardeman (1975), Somnath Datta (1988), Jagadish Gogate (1989), ChitraGunawardena (1989), Mostafa Mashayekhi (1990), Suman Majumdar (1992), Jin Zhu (1992) and Zhihui Liu (1997). Mostpursued academic careers and some ended up at research universities including Pennsylvania State, Columbia, MichiganState, UC-Santa Barbara, Guelph, SUNY-Binghamton, Iowa State, Louisville, Nebraska-Lincoln and Connecticut-Stamford.It was in the Army in 1944 that Jim read his first statistics book. It was
War Department Education Manual EM 327,An Introduction to Statistical Analysis , by C. H. Richardson, Professor of Mathematics, Bucknell University, published byUnited States Armed Forces Institute, Madison, Wisconsin (CQ).
Key words and phrases:
Hannan consistency, repeated games, compound decision theory, empirical Bayes.
Dennis Gilliland is Professor, Department of Statisticsand Probability, Michigan State University e-mail:gilliland@ stt.msu.edu. R. V. Ramamoorthi is Professor,Department of Statistics and Probability, MichiganState University e-mail: [email protected].
This is an electronic reprint of the original articlepublished by the Institute of Mathematical Statistics in
Statistical Science , 2010, Vol. 25, No. 1, 126–144. Thisreprint differs from the original in pagination andtypographic detail. D. GILLILAND AND R. V. RAMAMOORTHI
1. ST. JEROME HIGH SCHOOL 1935–1939 Q. Where were you raised? A. I was raised in Holyoke, Massachusetts by myfather and my mother’s sister. I was an only child;my mother died shortly after my birth. I went toSt. Jerome’s High School in Holyoke, a long blockfrom where I was living. The juniors and seniorspreparing for college were combined into one classfor two years of courses. The second year coursescould not build upon the first year courses. Q. I recall meeting you for the first time at a statis-tics department picnic in 1963. I was impressed bythe fact that you brought a glove and the way youplayed the game. Did you participate in sports inhigh school? A. The debate coach (priest) was the baseballcoach, and he was enthralled with the logical way Ilaid out a debate. He was an ex-pitcher who startedcoaching me in pitching. I think he was impressedwith the logic of my arguments. I had a basic knowl-edge of Aristotelian logic without realizing it. I wason the debate team and the baseball team. Q. We have seen your debating skills exhibited infaculty meetings over the years. Were you the beststudent in your high school class? A. Probably so.
2. ST. MICHAEL’S COLLEGE SEPT 1939–DEC1942 Q. Did you go to Mt. Holyoke College? A. No. The only time I had anything to do withMt. Holyoke College was when I went there to takethe Graduate Record Examination or something likethat. Q. Where did you go to college following highschool graduation in 1939? A. I went to a small college in Vermont. I hada scholarship from my high school that was onlypayable at a catholic college. I went to St. Michael’sCollege, which is about a mile from Winooski whichis about two miles from Burlington (laugh). Q. Did you spend 4 years at St. Michael’s? A. Well, when the United States entered the warin December 1941, colleges introduced paths for earlygraduation. Summer programs and acceleratedcourses were introduced. By the end of the fall of1942, I had earned 25% more than the required grad-uation credits and did not bother to attend the lastmonth of class. My degree came formally in January1943.
Fig. 1.
Jim at St. Michael’s College, 1942. Q. What was the degree and major? A. I earned the bachelor of philosophy (Ph.B.) de-gree and was a mathematics major. I was a patheticmath major (laugh). I avoided extensive courseworkin classical languages and the study of church reli-gion in Latin by taking the Ph.B. degree rather thanthe B.A. degree. Q. What was your exposure to mathematics at St.Michael’s? A. There was a first class mathematics instructorat St. Michael’s when I first went there in 1939, buthe disappeared the next year. His name was Andr´eGleyzal. He taught me pre-calculus from SutherlandFrame’s book. Gleyzal was not interested in doingany extra work. He simply had his grader stampyour homework AC, meaning accepted. Q. Was there a teaching style that influenced you?Were the mathematics courses rigorous at St. Mi-chael’s? A. There was an attempt at rigor, probably indifferential equations in the third year. And the manwho was teaching it didn’t understand it (laugh). Q. This was clear to you and few others? A. This was pretty clear. He was from St. LouisUniversity and working in some area of geometryand this is not much of a recommendation for hisanalysis.
CONVERSATION WITH JAMES HANNAN Q. Were your extra credits at St. Michael’s inmathematics? A. There were not many math courses there. Mylast year I was taking courses in solid and analyticgeometry and some course in classical algebra. Theydidn’t have a regular faculty member in mathemat-ics then; there was a graduate of St. Michael’s whoserved as part registrar and math teacher. He was abright guy, but he had no perspective. Q. Had you heard of statistics by the time yougraduated from college? A. No. Q. How many students were at St. Michael’s then? A. I would say about 125 students, now it hastwenty times that number I suppose. Q. Did you go back and forth to home very often? A. It was a long afternoon hitching rides. With nosuccess by evening, we headed to the train depot. Q. You mentioned that the US entry into the waraccelerated your undergraduate education. How didthis work? A. St. Michael’s offered fall semester courses inthe summer and used the fall for courses that wouldordinarily be offered in the spring. Q. Was the intervention to get students throughso that they could serve? A. It was probably more the case that they werehelping students graduate before their defermentsexpired.
3. US ARMY DEC 1942–DEC 1945 Q. Did you go directly from college into the Army? A. As I mentioned earlier, I stopped attendingclasses in December 1942. I managed to bypass mydraft board by volunteering for training in meteo-rology in the Army. The training program in mete-orology was nine months, the longest one that theArmy offered (laugh). I was told that the trainingwas to take place at one of four prestigious univer-sities, either Massachusetts Institute of Technology,California Institute of Technology, The Universityof Chicago, I have forgotten the fourth. Q. Where did you go for training? A. It was not at any of the aforementioned uni-versities. It was at the civic center in Grand Rapids,Michigan. No explanation was given to us. It wasclear that the Army had made some mistake in train-ing numbers and was forced to send the recruits toplaces where they received less training. The civiccenter had been taken over by the Army, as was adowntown hotel that served as the dormitory.
Fig. 2.
Jim’s Army Manual in Statistics, 1944. Q. Did it go the full nine months as promised? A. Yes, but study was not very compatible withthe required physical training. We were so exhaustedafter physical training that we went to our rooms tosleep; there was no study. Classes would end at 4 pm.Then they would march us in our units through theGrand Rapids streets up to John Ball Park for drill.I qualified with the carbine, both in shooting andin stripping the weapon. I also qualified with the 45caliber hand gun. You couldn’t hit a barn with it,but got used to the recoil. Q. How many were in your cohort? A. I think that there were about 300 of us. TheArmy had a handle on mass production. The Armygave us examinations and I think that I turned outto have done fairly well in mathematics, surprisingly. Q. Did you rank first on the mathematics exam? A. No, I didn’t but I scored in the top 10%. Thiswas a surprise to me. Among the trainees were men
D. GILLILAND AND R. V. RAMAMOORTHI from the East Coast and New York City who weremuch better educated in mathematics than I was.Apparently I created more of a good impression withthe Army by scoring rather high on an IQ test. Q. When were you commissioned as a Second Lieu-tenant? A. Upon completion of training in the fall of 1943.The Army found out by this time that it had trainedmore meteorologists than it needed. Q. We presume that this could have been badnews. A. Yes, but the Sergeant had already turned inthe roster with me assigned to the Army Airbase atLewiston, Montana. When I arrived at Lewiston, Ifound that the base was five miles away. I had neverlearned to drive. However, people put me in a Jeep,pointed me in the right direction, turned on the key,and told me to turn off the key when I arrived atthe base. Q. What was your position at the base? A. I was already commissioned and qualified as ameteorologist. At the base, I was supervised by theperson who ran the weather station. The work as ameteorologist was made somewhat complicated bythe fact that the information and forecasts had tobe coded. The Army thought that someone could belistening and learning something about the weather.There was a different code for every day. Q. We suppose that you created graphs with sym-bols indicating various information, for example, ar-rows indicating wind velocity. A. Yes, I did. We used the Beaufort system usingnumber of dashes for wind speed. I had learned thesystem but not with ease. Q. What was life like on the base? A. We lived on the base in wooden barracks. Therewas an officers’ mess hall. There a second lieutenantdoes not get much respect, none from below, littlefrom above. Q. How long were you at Lewistown? A. Only about four months. For some reason, I ap-plied for tropical weather training. The Army pulledme out of Lewistown about Christmas and sent meto Miami, Florida to await duty assignment in SanJuan, Puerto Rico. I then spent three or four monthsthere in fulltime advanced study of tropical meteo-rology. Q. Did you ever get feedback on your forecastsbased on the outcomes? A. (Laugh) Yes, I recall one case when I was backin the United States. I gave a notoriously bad fore-cast. I had forecasted that the low cloud cover would rise up and blow away. The pilot took off based onmy forecast and radioed back from ten thousand feetthat it was solid all the way up. Q. Was the feedback from outcomes useful? A. Yes, but mainly it helped us recognize how faroff forecasts could be. Q. What was your next assignment? A. I was sent by ship to Bombay (Mumbai), In-dia. I recall being in the harbor there in May 1944after a very long ocean voyage. Along the way westopped in Algeria and waited a week to transfer toa British ship for the remainder of the journey. Aswe traversed the Mediterranean, I served as officerof the day once. This was not duty that one sought.You were required to inspect the prisoners in thebrig and every nook and cranny on the ship and beon deck while everyone else was posted below. Q. What happened following your leave from theship in the harbor at Bombay? A. Rooms were provided in the city. Orders ar-rived in a week starting with a three day trip acrossIndia to Calcutta (Kolkata) on a troop train. Thetrain was rather open to the elements. It was veryhot and at the onset of the monsoon season. Rainblew into the train. I was as sick as a dog; practi-cally everyone had an infection of sorts. When wearrived, I did not realize that I was in the vicinity ofa place of statistical significance, the MahalanobisEstate in Barrackpore. The Estate was eventuallyturned-over to the Indian Statistical Institute. Q. Have you ever visited the Indian Statistical In-stitute in Barrackpore? A. No. Q. How long did you stay in Calcutta? A. I probably stayed a week or two in Calcuttabefore being sent to a small village, Gushkara, thatwas 150–200 miles to the northwest. There I was incharge of the meteorology set-up. I was the only offi-cer at the weather station. I only spent a few monthsin the village. The village had an air strip and servedflights in and out of China. It was a pretty quietbase. Information came in over the radio in code.Teletype had not reached the village yet. Q. Do you have other recollections of your stay atGushkara? A. I recall that I had a dentist friend there onthe base who fixed up my teeth with early morningappointments. Q. At some cost? A. No, because he was a friend and a fellow bridgeplayer. Actually, it was poker that served me well in
CONVERSATION WITH JAMES HANNAN the army. My poker playing started on the trip toBombay. There were poker games below deck. Therewere games going the entire journey. I was forced toleave the games that one day when I was officer ofthe day while traveling across the Mediterranean. Itwas pretty much just playing poker, having regularmeals and sleep. I would stay below deck for daysat a time. Some of the games had pots that built upto a couple of hundred dollars. Q. Apparently, you did not get to see much scenery. A. Well, going through the Suez Canal I did onceventure on deck. About all one could see from theship were the banks of the Canal. Q. Did the Army discourage this gambling? A. No. In fact, at every base I was at there werecard games going in the officers’ mess. You couldpretty much find a game whenever you wanted. Q. Where did your next orders take you? A. I was ordered to proceed to China to join thecombined Chinese American forces. We flew “overthe hump” to the base at Yunnanyi. I have kept asmall diary that indicates we arrived on March 23.I then drove a Jeep to the air base at Kunming, ar-riving on April 12. This was a major base and farenough from the enemy forces to not be in danger ofbeing over run. I kept the Jeep to eventually deliverto a base in Chihkiang (Zhejiang) close to the frontlines. I recall that the last base was within 50 milesof Japanese forces. It was a dangerous place with en-emy forces dressing as coolies to infiltrate the area.From this base, the air missions were very short andin support of ground operations. That base had anevent that made an issue of Time magazine. Thecommanding officer had mercifully shot an Ameri-can pilot who was trapped in a burning plane. Therewas an official court martial but the commanding of-ficer was exonerated. Q. What was driving like across China? A. There were mountain roads with lots of switch-backs. It was a dangerous trip. It felt as if we weregoing vertical on the turns and always coming closeto turning over. There were no roll bars on the ve-hicle. Q. What were your major responsibilities as a me-teorologist at these bases? A. Generally there were two meteorologists to manthe weather station, each working a 12 hour shift.I sometimes pulled the night shift. Our responsibil-ities included analyzing data and giving advisoriesto flight crews leaving the base. Q. Did you ever forecast using a probability, say,70% chance of rain? A. No. But sometimes forecasts were hedged byputting conditions on them such as “if this, thenthis.” At some point our forecasts came from search-ing historical records to find days where conditionsmatched those of the current day. We then forecastwhat was typically observed the following day. Q. Something like play against the past ? A. Yes. Actually, I believe that the success of weatherforecasting today comes from the availability of com-puters to solve large systems of thermodynamic equa-tions. It is a long way from looking at the sky andputting up your finger. Q. Were you kept busy? A. Sometimes we were behind in our work. Othertimes it was make work to keep us busy. Q. When did you depart from China? A. After about three months at my last base, wereceived word that the war had ended. This was inAugust 1945. They moved us to the coast to awaittransport to America. While waiting, I saw Japanesesoldiers as prisoners being marched through the streets.Eventually we were taken to Shanghai and we de-parted by ship to Seattle, probably in November.This ship was much faster than those that took usto Bombay. From Seattle I went by train to FortDevins, Massachusetts to be discharged. You mightsay, “Around the world in two years.” Q. Did you play poker on the trip from Shanghaito Seattle? A. (Laugh) Probably not. I think that I had expe-rienced some bad nights in China and by this timewas not playing poker. Q. But you still came back with winnings? A. Oh, yes. I had banked about two thousand dol-lars which eventually helped to support me throughgraduate programs. Q. You were commissioned as a Second Lieutenantas you graduated from your meteorology training.Did you leave the Army as a Second Lieutenant? A. (Laugh) No, I left as a First Lieutenant; not ev-eryone receives many promotions as you win a war.In fact, a base commander, a Major, ran into heavyweather and blamed the weather forecaster. This didnot help my chances for promotion. However, I didleave with a warning about tuberculosis. I do not re-member being too concerned, but I thought otherswould be concerned, particularly, those about me. Q. Did you consider a career in meteorology?
D. GILLILAND AND R. V. RAMAMOORTHI A. No. The training was minimal compared towhat may be available today. Q. What occupied your time until you startedgraduate school? A. When I returned to Massachusetts in December1945, I applied for Harvard, fall 1946. As a somewhatdelayed reaction, I decided to start in the summerof 1946.
4. HARVARD JUNE 1946–JUNE 1947 Q. When did you become aware of statistics? A. I guess there was that Wisconsin Army Text,really an old classic of sorts. At Harvard I took a twosemester course in probability and statistics fromVon Mises. He was the instructor. Q. Were you working on a master’s degree? A. Yes, I was rather rusty at that point. When Iwent to Harvard in the summer of 1946, I took afull program. There was an instructor visiting fromBerkeley by the name of Wolfe. He taught a coursein differential equations and it (laugh) was a realcourse. I was not very good at it, but luckily therewas a bunch of teachers in the same class and theywere worse (laugh). Well, we were using Ince as asource, a classical book; and we did construct solu-tions. Q. Do you recall the other courses that you tookat Harvard? A. I took a course in projective geometry in thesummer of 1946 which I did not understand verywell. I had a full program in the fall of 1946 and thespring of 1947. I had complex analysis from Alfors. Itook a two-semester course in modern algebra fromGeorge Mackey who was well known for his researchin various fields of abstract mathematics. We usedthe textbook by Birkhoff and Mac Lane.Then I had another course in the mathematicsof physics. Birkhoff ended up teaching the secondsemester of the course. The first semester was taughtby Van Vleck, who was a mathematician of sorts,but he was more in applied math. Q. Which Birkhoff taught that second semester ofmathematical physics? A. Garrett Birkhoff. Garrett is famous for his workon lattice theory and for working with Mac Lane.Garrett’s father, George Birkhoff, was more famousfor his work in differential equations, but he wasn’taround at that time. Q. What was the mathematical physics course like? A. It was classical Fourier series and special func-tions. Q. Was Harvard on the semester system? A. Yes, but in the summer session there were fewregular Harvard faculty teaching courses; most ofthe teachers were visitors. Q. Did you take courses at Harvard in the summerof 1947? A. No, I graduated in the spring of 1947. I justeked through the masters. The masters was a con-demnation then. Q. Were you thinking about the Ph.D.? A. I was thinking about it. Some of my fellowstudents were intending to go on for the Ph.D. anda few of them made it. Q. Having completed the masters, did you con-sider a nonacademic career path? A. No, I was intent on pursuing the Ph.D. I ap-plied to about 10 or 12 graduate schools to startstudy in mathematics in the fall of 1947. The schoolsincluded Columbia, Princeton, Yale and the Univer-sity of North Carolina. I was accepted by some, re-jected by others. I was accepted into the Ph.D. pro-gram in statistics at the University of North Car-olina for the fall of 1947. I believe that Yale andPrinceton turned me down. Later I met persons atPrinceton and they explained that Princeton had asmall quota. They could fill the quota with appli-cants much better that I was. Q. Had you decided to concentrate on a particulararea of mathematics? A. No, I had no idea, but I had been influenced byVon Mises at Harvard. He was a professor of aero-nautical engineering. He was serious, deliberate andinsistent upon following his approach. He was moreinto the philosophy of randomness and foundations.He had postulates but the stuff didn’t work. Hiscourse did lead us slightly into statistics.
5. UNIVERSITY OF MICHIGANJUNE 1947–DEC 1947 Q. Why did you go to the University of Michiganin the summer of 1947? A. I realized that I needed more course work be-fore starting my doctoral program and went to AnnArbor in the summer of 1947. It was one of a few uni-versities that I knew of that offered summer coursesof interest to me. I figured that it would be goodpreparation. I went there with the intention of stay-ing for the summer only, but the routine, requiredphysical examination revealed the spot on my lungand the possibility of tuberculosis. This caused me
CONVERSATION WITH JAMES HANNAN to stay through the fall of 1947 as my condition wasbeing followed. Q. What courses did you take in Ann Arbor? A. I took some basic math courses. One was a sec-ond year modern algebra course and another was acourse in group representations by Richard Brauer,which I dropped later. Probably, I had to enroll ina number of courses to keep my GI benefits. Therewere about twenty faculty sitting in and three stu-dents enrolled. The faculty had much more appreci-ation of group representations and what they weregood for. Brauer was so smooth that you could leaveclass convinced that you knew the subject when youreally did not. Q. You mentioned courses on the algebra side yetyour academic career shows more work on the anal-ysis side. A. I also took the real variables course from Hilde-brand. He was somewhat of a source of inspiration.I took a statistics course from Dyer and C. C. Craig.They were both Ann Arbor products. Howard Raiffawas a student of Dyer. . . Dyer’s prize student. I didnot take a course from probability people. Q. Was the Dyer and Craig course a mathematicalstatistics course? A. It was theoretical from the point of view ofnonmathematicians. It was not very satisfying. C.C. Craig did stimulate me to think about poolinginformation. We had a small class. Each day when hecame to class he would rattle coins in his pocket andchallenge us to make estimates concerning the coinsin the pocket that day. He was trying to convinceus that one could not use the Bayes theorem in ameaningful way. (Laugh) It is very hard to prove anegative result. Q. Any other recollections regarding your stay inAnn Arbor? A. I played bridge regularly. Once I bid “three no-trump” and an opponent was sitting over me with allfour aces. I made the contract. I recall when ThomasDewey visited Ann Arbor. He walked through thecenter of the quad. People were out sunbathing andsimply looked up as he went by. It did not causemuch of a stir.
6. VETERANS HOSPITAL JAN 1948–MAY1948 Q. How was your time spent after you left AnnArbor in December of 1947 and until you enrolledin statistics at the University of North Carolina inthe fall of 1948? A. You recall that I had stayed in Ann Arbor inthe fall of 1947 to have the spot on my lung followed.In January 1948, I entered a Veterans Administra-tion Hospital in Framingham, Massachusetts for pos-sible treatment. There I spent time in a facility fortuberculosis patients, waiting “recovery” to start mygraduate studies. The spot was actually gettingsmaller, and the fact that it was changing causedgreater concern about my condition. Eventually Iwas released when it was decided that I did not haveor was clear of tuberculosis. Q. How did you keep occupied in the hospital; didyou play poker? A. No, I took the time to study end games inchess. I did not play chess but enjoyed the studyof end games. I treated end game play puzzles asmathematics. I did not read mathematics when atFramingham. We were kept in bed and nourished. Iwas there about 2 months. Toward the end I was al-lowed to leave on weekends—I recall going to Bostonon a couple of weekends. I did not have a car.
7. UNC AUG 1948–AUG 1950 Q. Did you enter the University of North Carolinain the fall of 1948 with an assistantship? A. No. But I had support under the GI Bill andfrom my poker winnings. I was soon given a re-search assistantship, more of a fellowship. They hadno need for teaching assistants. Q. Who were your fellow students there at UNC? A. Raj Bahadur, Sutton Monro, Ralph Bradley,Ingram Olkin, Shrikande, . . . . Q. We understand that you met your future wife,Bettie Meade Creighton, at UNC. A. She was a graduate student working as a sec-retary to Hotelling, having worked previously forthe Dean of the Graduate School. Hotelling was im-pressed with her considerable skills with dictationand shorthand. We were married in 1951. Q. What courses did you take during your twoyears at UNC? A. The courses were small at UNC with ten orso students per class. I recall taking a course ineconometric models and least squares from HaroldHotelling. He was more or less at the end of his ca-reer. I did learn why if you find five shoe stores in amall, four of them will be clustered close together.I took two courses from E. J. G. Pitman. He hadmathematics and Pitman “efficiency.” I took prob-ability and applications from Herbert Robbins my
D. GILLILAND AND R. V. RAMAMOORTHI
Fig. 4.
Bettie and Jim on wedding day, 1951. second year. Of course, he became my thesis direc-tor. I had S. N. Roy for a course. Wassily Hoeffdingtaught nonparametrics. He influenced me consider-ably and was a serious reader of my thesis that camethree years after I left UNC. I taught Hoeffding howto drive while at UNC. Years later, I taught Pitmanhow to drive while visiting Stanford. He had to keepbeing reminded that in the United States we driveon the right-hand side of the road. Q. Why did you leave before writing your disser-tation? A. I decided that I needed teaching experienceand went to Catholic University in Washington, DC.There I taught abstract algebra from Birkhoff andMac Lane, a course in differential equations and areading course in statistics. Q. Your 1953 UNC thesis [18] contains several re-sults, some in compound decision theory for sets ofstatistical decision problems, some for symmetriza-tions of product measures, some concerning averagesof empirical distributions from independent but notnecessarily identically distributed random variables.It is curious that your later work in repeated gamespublished in 1957 is directly relevant to forecasting,specifically, selecting the best forecaster from a setof forecasters based on the history of errors. A. When I went to Robbins, I explained my in-terest in the challenges posed from pooling acrosssequences of decision problems, perhaps, having theC. C. Craig challenge in mind. Robbins quickly de-termined that he could deal with sets of decisionproblems. His results on compound decision theorywere published in the
Second Berkeley Symposium [27] and part of my thesis dealt with bounds andrates in compounding general two-state problems. Q. What topics did you study under Robbins? A. Robbins was teaching probability and analy-sis, but he was interested in certain applications ofprobability and probably ended up concentrating onthose and not going as deeply into general theory.He had a free hand and taught whatever he wanted. Q. At some point in the spring of 1950 you securedthe position at Catholic University. At that pointdid you have a thesis topic in mind? A. Yes, more or less to extend Robbins’ result oncompound decision theory with a general proof forthe two-state problem. I believe that Robbins pub-lished his compound decision problem in the
Sec-ond Berkeley Symposium . The only inversion wasthat Robbins had both the empirical Bayes formu-lation and the set compound formulation in mind in1950. He could only give one talk and thought that
CONVERSATION WITH JAMES HANNAN the compound decision result would create a big-ger splash. He gave the empirical Bayes talk at the Third Berkeley Symposium [28]. (For an introduc-tion to and review of the compound and empiricalBayes decision problems, see Zhang [38].) Q. You mentioned talking to Robbins in your sec-ond year about compounding in the sequence case.How did he react? A. Robbins mentioned that, with the entire setof data available before all decisions were made,one could estimate the empirical distribution of thestates. But that when only initial segments wereavailable at each stage, the problem is more diffi-cult. Q. In his
Second Berkeley Symposium paper, Rob-bins does give you credit for some computationsso you must have been actively involved with thecompound problem before leaving in the summer of1950? A. Yes, but the computations were wholly of in-terest to him because they concerned the examplehe had of testing one specific normal versus anotherand he needed the computations. Q. You mentioned C. C. Craig at the Universityof Michigan challenging the students to explain how
Fig. 3.
Jim at UNC, 1949. the information coming across days from the rat-tling of coins could be pooled to improve estimates.When you first discussed pooling (compounding)with Robbins, did the discussion trigger somethingin Robbins or was he already on the trail of com-pounding? A. Well, he was on the trail of a method butclaimed that he could not do it. This was a strongstatement that, of course, was wrong. He could anddid demonstrate it. Q. For the set compound formulation not the se-quence version? A. Yes. I believe that Robbins did not push thesequence version of compound decision theory un-til he had Esther Samuel as a graduate student atColumbia. After she had come to the point of finish-ing her thesis, Robbins suddenly remembered thatI had done something on the sequence problem. Hebecame worried about her losing her thesis and con-tacted me. She did not. Q. Did Robbins get into the compound problemin his course? A. Well, he was trying to talk about it. Q. Your thesis dealt with the compounding acrossa set of two-state (testing simple v. simple) decisionproblems. A. Yes, and some other things. Q. The results in symmetrizations of product mea-sures? A. Yes, that relates to the second chapter. How-ever, I didn’t put it together as a final result withthe strong properties that I sought. Q. Did you ever publish that work on symmetriza-tions? We recall that some of your students mayhave worked on this as well. A. I did not publish it at the time, but I did getseveral of my Ph.D. students onto some of the re-maining research challenges. Q. The symmetrizations result was a critical toolin showing the asymptotic closeness of the simpleand equivariant envelopes and in attacking the Rob-bins’ conjecture that eBayes procedures would solvehis compound problem. A. Yes, that is true. Q. At the time you left UNC after only two yearsof study, was your thesis coming together? A. No, I was struggling and not getting the resultsI thought I could get. However, I already had accom-plished the Kolmogorov–Smirov work that was laterto become Chapter 3 of my thesis. D. GILLILAND AND R. V. RAMAMOORTHI Q. What were your classmates at UNC research-ing? A. Bahadur was trying to interest Robbins and assoon as Robbins got a glimpse that Raj was quitetalented, he became interested. Raj had his ownproblem, the “problem of the greater mean.” Q. What about the others? A. I believe that Shrikande worked with R. C.Bose. Bradley may have worked with Hotelling.Vohra was an early Ph.D. and I think that he workedwith Hoeffding. Hoeffding ended up with a coupleof good students the year after I left. Monro wasthere. He became interested in the Robbins’ infer-ence problems. Ingram Olkin was a graduate studentduring my first year. Q. Was there a social life there involving the grad-uate students? A. There was sort of a split. There was an In-dian unit among the graduate students includingBahadur, Shrikande and Chanti Vohra. The nativeswere a motley crew including Bradley, Monroe andmyself. There was a split in the sense that the In-dians had deeper training. Ralph Bradley may havebeen an exception, but he was Canadian.In Chapel Hill at that time, the Indians were aspecial case. Chapel Hill was segregated then. Somegot into private homes where the landladies madesure that they were to be thought of as Indians andnot blacks. Bahadur resided in graduate housing,and it was the persons in graduate housing that Igot to know. I rented a room in a private home thatwas near to the building that housed statistics.At some point George Nicholson replaced Hotellingas chair. During the war, Nicholson had tent mates
Fig. 5.
Jim’s MSU Application Photo, 1953. on Guam that were statisticians in operations re-search. When I left I was sharing an office with RajBahadur and even his hours. I would stay up halfthe night (laugh). Q. Were you smoking then? A. Yes, and Raj was as well. Q. Did you play tennis at that time. A. Yes, with Raj and he was more adept at it thanI. Q. In Robbins’
Second Berkeley Symposium paper[27], he gives examples of and motivations for com-pounding. Did you leave UNC with the idea that youwould develop compound decision theory to covergeneral component problems? A. As you know, the compounding part of my the-sis concerned two-state problems with some of thework published with Robbins as co-author [17]. Ihanded-off the m-state problem to John Van Ryzin,one of my first graduate students, and with him pub-lished the paper on improved rates for compoundingthe two-state problem [13].
8. MICHIGAN STATE UNIVERSITYSEPT 1953–PRESENT Q. How did you happen to come to the Depart-ment of Mathematics at Michigan State Universityin 1953? A. Leo Katz was a visitor at UNC from MichiganState University and he encouraged me to apply.Also Ingram Olkin was now at Michigan State Uni-versity, and he encouraged me to apply. Olkin wasa Columbia M.S. and took his Ph.D. from UNC. Q. We have had a chance to read the letters ofrecommendations from Robbins, Hotelling and Ho-effding in support of your application for an ass-sitant professorship at Michigan State University.Were you the top student in your cohort at UNC? A. Remember that Bahadur was not in those classes.That is one explanation for the strong letters. Thestudents from India came with strong backgroundsand were advanced to the point that they did nottake some of the classes that I took. Q. Did you interview at places other than MSU? A. In those days you did not go out and interview.Schools were hunting for personnel rather than theother way around. Q. It is curious that your MSU application formasked the applicant about high school teaching ex-perience. You admitted to none. When you arrivedwhat was the teaching load?
CONVERSATION WITH JAMES HANNAN Fig. 6.
Michigan State University Department of Mathematics, 1955. Bottom row: 8 from right—Sutherland Frame, 4 fromright—William Harkness, 3 from right—Ingram Olkin. Second row: 6 from right—Leo Katz, 5 from right—Ken Arnold. Toprow: 6 from right—Jim Hannan. A. It was 12 hours/week, although some seniorpersons might have had less. We were on the quar-ter system and the courses could be either 3 or 4credits. The slide rule course was a 1 credit course.When I came, Sutherland Frame was chair of the De-partment of Mathematics. I had used Frame’s pre-calculus textbook at St. Michael’s. Q. Who were the members of the statistics groupwhen you arrived? A. When I came, the statistics group included LeoKatz, Ken Arnold and Ingram Olkin. Baten had anappointment in the Experiment Station as a veryapplied statistician. It was rather shocking when hegave a talk in which he described taking a randomsample of trees and saying that they came out “realrandom.” Oh, Charles Kraft came the next year. Hehad left Berkeley because of the strike at Berkeleyrelated to the government’s anti-American activitysearch. He did a thesis with LeCam. Gopi Kallianpurcame in 1956, and he came down with tuberculosis. Irecall visiting him in a Lansing hospital. Jim Staple-ton and Martin Fox came in the late 1950’s. Herman Rubin and Esther Seiden came a little later. Kraftand Olkin were only in the department a short time. Q. So you were here when the Department of Statis-tics was created in 1955. A. Yes. Frame served as chair of both departmentsthat first year. There was a dichotomy. It was recog-nized that the statistics faculty could teach elemen-tary math courses, while the math people could notor were uninterested in teaching elementary statis-tics courses. Q. One of the documented reasons for the creationof the Department of Statistics was the fact the fac-ulty in statistics would be expected to consult andwould, therefore, have a lesser teaching load. Didyou have consulting opportunities? A. Yes, early on I did work somewhat collabora-tively with Clifford Hildreth of Economics. He wasanxious to add more mathematics to his research.This did not lead anywhere. He later became an Ed-itor of the
Journal of the American Statistical As-sociation . D. GILLILAND AND R. V. RAMAMOORTHI Q. Who were your early collaborators in basic re-search? A. The first chapter of my thesis was published in1955 in the
Annals with Robbins as my co-author[17]. When I came to Michigan State University in1953, I began a collaboration with Jerry Gaddum,who was in geometry. Blackwell had sent somethingof a mathematical nature to Gaddum, and I helpedhim prove something. I then started generalizingit so much that Gaddum was less happy, and hedropped out of the research into repeated games. Hewas interested in linear programming but not gametheory. Gaddum is acknowledged in my 1957 paperin
Contributions to the Theory of Games [15].Early on I collaborated with Herman Rubin ona technical report titled “Sigma-fields independentof sufficient sigma-fields.” He okayed my proof andhad good knowledge of the literature that I did nothave. I did not work directly with others at MSUat that time. Over the years I collaborated in re-search with a number of my graduate students andothers including Ronald Pyke, E. J. G. Pitman, R.F. Tate, Gordon Simons, V´aclav Fabian and R. V.Ramamoorthi. Q. Perhaps now you are best known in the pro-fession for your 1957 game theory paper [15]. Thispaper is often referred to in recognition of your hav-ing developed strategies for repeated play of a gamethat have a property now called
Hannan consistency [19]. At the same time, David Blackwell was estab-lishing an almost sure result using his approachabil-ity theory [1]. What was going on? A. Of course, this research was related to some ofmy doctoral research. The research under Robbinswas on sets of statistical decision problems. In the1957 paper I was dealing with sequences of gamesrather than sets of statistical decision problems. Idid not recognize approachability theory as apply-ing. I let Blackwell know when I completed the gametheory work. He suggested that I publish my resultsin the Princeton University Press series, which I did.Blackwell’s recognition of the use of his approacha-bility theory to get the envelope result came later,but he did get it into his publication [2]. Blackwelldid alert me to the fact that approachability theorycould be used to prove results on convergence to en-velope risk. Someone told me, I have forgotten who,that Blackwell had announced some results that ei-ther contained or were related to mine and men-tioned that I had priority. This was at a meetingsomewhere. Q. Have you ever used your game theory resultsin your personal decision-making? A. I can’t say that I have (laugh). I suspect thatcompounding is being actively used. Economic the-orists have been using it but without the mathemat-ics. Q. Did you have leaves from MSU that took youaway from East Lansing? A. I went on leave to Stanford for the year 1956–1957. They had openings for persons to work oncontracts from the Office of Naval Research. I dida few things related to those that didn’t lead any-where. Herman Chernoff was sort of acting as anoverseer of the contract work. I recall that the con-tract work dealt with logistics of keeping ships sup-plied. Too many persons were deciding what a shipneeded and my work was on creating discipline in in-ventory and stocking for naval vessels. Some of theinventory problems were amenable to compounding.Bellman was at the Rand Corporation and had al-ready done some related work but I did not makeconnections with him. Karlin had been at Rand. Q. Julia Robinson [29] proved that in a two playergame if both players use the play against the paststrategy , then average risk converges to the value ofthe game. This is called fictitious play . She creditsBrown at the Rand Corporation for the idea. Didyou correspond with Robinson? A. No. Her husband Raphael Robinson was onthe mathematics faculty at Berkeley. She did notget any recognition until the fictitious play paper.Eventually they gave her an appointment. Neymanpushed her into the National Academy of Sciences.His name carried some weight. Q. Was there any reaction to your game theorywork from the research community? from the RandCorporation? A. Bowker and Karlin at Stanford were interestedin the fact that I had work related to Blackwell.People at Rand probably had limited command ofwhat Blackwell had done and an interest in otherthings that they had better command of. Q. Did you interact with others at Stanford? A. Well, E. J. G. Pitman was there. He was atChapel Hill my first year and then at Stanford whenI visited. I helped him find a car and taught himhow to drive on the “wrong” side of the road. Hebought a car that was ancient enough for him to feelcomfortable with. His car had a stick shift; he didn’twant any additional complications. I worked withhim on a moments problem. We put out a technical
CONVERSATION WITH JAMES HANNAN report and did not publish elsewhere. Birnbaum hada student who came up with similar results at aboutthe same time. Q. Others? A. Samuel Karlin had two offices down the hallfrom me. We had rather immediate contact in regardto his monotone likelihood ratio work. I knew a fewthings and kept finding theorems where the proofsdidn’t quite hold together. He may have stretchedthe Royden integration theory a bit. I probably both-ered him some. I recall him being anxious to getto his bridge games that started at the lunch houron Fridays and sometimes lasted late into the af-ternoon. Vernon Johns was a student of Robbins atColumbia and was then at Stanford as a regular fig-ure. He collaborated with a Donald Guthrie and alsowith Karlin and Olkin on occasion. Ruppert Millerwas a first-rate thinker and was often the one to getthings worked out. Q. Did you meet Thomas Cover while at Stanford? A. Yes, at a meeting and we spent two hours in anoisy room discussing problems. Q. Did you teach at Stanford? A. In addition to working on the project, I taughttwo quarter courses plus a one quarter course inadvanced inference using Lehmann’s Notes. I hadalmost all of the advance graduate students in myclass including William Pruitt and Donald Ylvisakar.Pruitt went to the University of Minnesota and diedrather young. Q. Did you meet with David Blackwell while youwere on the west coast? A. I first met Blackwell when he invited Bettieand me to a lunch with him and his family while Iwas visiting Stanford in 1956–1957. We chewed upa lot of the family dinner. His wife was a very goodcook and she pushed lots of food on me. Anyway,when we met for lunch, it was a long affair and hehad committed to a seminar following it. Q. Any other recollections of your time at Stan-ford? A. When I gave a talk on the west coast, CharlesStein kept me on the right track to finish my proof.I refer to him in my game theory paper for unpub-lished work on the prediction of a binary sequence.Stein was at Stanford and the talk was probablyat Berkeley. Stein’s inadmissibility result was pre-sented at the Third Berkeley Symposium in 1955[31]. Sometime later I sent Stein a note that I thoughtthat, in analysis of variance, the intraclass correla-tion would be a case where compounding would ap-ply. Subsequently, he published results on this. The James–Stein [21] and Efron–Morris [5] connectionsto empirical Bayes came later. Q. Was other research accomplished during your1956–1957 leave to Stanford? A. My research into maximum likelihood estima-tion of discrete distributions was started at Stan-ford but was probably motivated through discus-sions with Lucien LeCam. It was published in [12]as a chapter in the Hotelling Volume. Q. Was John Van Ryzin your first Ph.D. student? A. No, earlier I had a third of William Harknesswith Katz and Olkin. I also had a half of ShashikalaSukatme. Her husband was in our department. Shestarted with Olkin, and I took over when he left.John Van Ryzin left short of thesis, but he finishedmore quickly than I did after I left UNC. That wasanother one of these things that does not explainitself adequately. He had actually worked on condi-tions for improved rates for the two-state problem,but I had done it for the m-state. We agreed to splitit so that we published the two-state jointly, andhe published the m-state (set version) solely. I feltthat the latter was more likely to be accepted forpublication. Q. We notice that he moved quickly to the se-quence version of the m-state. It came out in the
Annals as Van Ryzin [32], the same year as did hisset version m-state [33]. Didn’t another of your stu-dents leave short of thesis? A. Yes, V. Susarla went to the University of Wis-consin, Milwaukee, in 1969 and finished his thesisin 1970. Van Ryzin was at Madison at the timeand ended his career as chair at Columbia. Susarlaand Van Ryzin became collaborators, and, tragi-cally, they both lived short lives [Van Ryzin (1935–1987) and Susarla (1943–1989)]. Q. In their memory you started the Van Ryzin–Susarla Fellowship for study in the Department ofStatistics and Probability at Michigan State Univer-sity.Over the years you collaborated with some of yourformer graduate students in resolving Robbins’ (1951)conjecture that decision rules that are Bayes versusdiffuse priors in the empirical Bayes problem willbe asymptotic solutions to both his empirical Bayesand compound decision problems. How did this re-search evolve? A. The research started in the early 1970s andappeared in technical reports and theses. Publishedresults with rates for finite state cases came fromcollaborations with Gilliland [9–11], Huang [10, 16] D. GILLILAND AND R. V. RAMAMOORTHI
Fig. 7.
Fig. 8. and Majumdar [24]. In other more general contexts,rateless related results were established by Datta [3,4], Mashayekhi [25] and Majumdar [23]. Q. You have recently reexamined the implicationsof results described in your 1956 abstract [14]. Howis this going? A. In that abstract, I describe an extension of myrepeated game results to the case of repeated sta- tistical decision problems. That extension uses es-timates for the empirical distribution of opponent’spast play and has implications for the less-than-fullmonitoring case described in Rustichini [30]. The es-timation issues naturally arise in compound decisionproblems. Vardeman [34, 35] works this out for thek-extended envelope problem [11].
CONVERSATION WITH JAMES HANNAN Fig. 9. Q. You collaborated with V´aclav Fabian in re-search and in writing your 1985 book
Introductionto Probability and Mathematical Statistics [6]. A. It was a very inefficient collaboration becausewe were never working together on the same thingfor the book. I anticipated disagreement with Fabian’swriting style but could not hold out, only argue formy style. Q. Bettie helped you have access to the Russianliterature before it was available in English transla-tion. How did that come about? A. Bettie was a graduate student in Art Historyat UNC but had no education in modern languages.Here at MSU she became very interested in Frenchand then Russian. The latter was partially inspiredby my need for translations. Q. Who were your teachers who most impressedand influenced you as a teacher? A. I think first of Richard Bauer for group repre-sentations. He was a magnificent lecturer. He wouldcome in and do the review of the week in 5 min-utes and it would be clear! He would then add to it.I was not appreciating fully all that was involved,but it all fit together so beautifully. I was naturallyimpressed with it all—it was such a large differencefrom what I had had in the past. Andr´e Gleyzalat St. Michael’s was slightly impressive, but he washolding back very much from what he could do. Histhesis came from Ohio State University in mathe-matics. Q. Concerning your own style, you are renownedfor the concise notation and connecting arrows inyour board work. A. I was not able to write fast on the chalkboardso I was accommodating that fact through my style. Q. You advised that one should not referee morepapers than one submits because refereeing shouldbe taken seriously. You had a reputation as a seriousreader and did more than your share of work to im-prove papers and theses. In regard to other serviceto the profession, how long were you the book revieweditor of the
Annals of Mathematical Statistics ? A. I do not recall. (It was 1966–1972, seven fullyears.) I do recall that Jack Keefer advised me toget competent reviewers and not to heckle them. Q. We have heard the Sir Ronald Fisher visitedMichigan State University in the late 1950s and gavea series of talks. What was that like? A. He gave a series of lectures. He had a new book(recent at that time) and wanted to talk about thebook the way he thought about the book and, Kraft,in particular, was more interested in mathematicalcontent. We had a conflict there. Kraft had definitetheorems in mind, and he could never get anythinglike that out of Fisher. Q. So Kraft spoke up regularly during the lec-tures? A. Well, he didn’t badger him very much, but Iknew what he had in mind. He worked with LeCamand worked at that level. Fisher was still back into D. GILLILAND AND R. V. RAMAMOORTHI thinking that everything he did was more importantthan anything any one else did. (Laugh) I think thatFisher had to maybe miss a few dates and then hecame back. He threw away his notes and proceededto tell us what he thought of the kind of statistics wewere doing. He said the Annals should be bundledup and deposited into “yon river,” the Red Cedar. Q. What would have given him this inspiration tosuddenly go on the offense? A. Well, he was getting embarrassing questions.We were willing to talk about his thing, but wewanted to talk about the mathematics of his thing.Of course, eventually we noticed that we were notgoing to get there and we shut up. It didn’t get toonasty at that point, only after he told us what hethought of us and what we could do with the
Annals . Q. Did he mention Neyman in his talks? A. I don’t believe so. He had already fought thatwar. Q. You are rather well known for your willingnessto carefully read the proofs of your professional col-leagues. It seems that you often find gaps, if notways to improve proofs. Early in your career, youdiscovered that Lemma 4.3.8 was false in the firstprinting of Samuel Wilk’s book
Mathematical Statis-tics [36]. This lemma was key to supporting theproofs of the asymptotic properties of maximum like-lihood estimators. How did you handle this discov-ery? A. I took an interest in Wilks’ book since I waslooking for a strong basis for asymptotics. I couldnot find it there. Wilks seemed to treat analysis asalgebra; I know since that is where I started out.The analysis was in Cram´er but he did not belaborthe point. I still have the correspondence. I wroteto Wilks in April 1962. I realized that the lemmawas false and that Wilks was getting too much fromtoo little. He thanked me for the letter and advisedthat within six months he would get back to me onthe issues that I had raised. This he did. In a letterin July 1962, Wilks writes, “You are quite right.False as stated. I am working on stronger conditionsfor the theorems that will make them applicable toparametric estimation.” Q. I understand that Wilks passed away beforethe second printing that corrected the situation andacknowledged E. J. Hannan for pointing out the er-ror. A. Yes. Wilks’ death was very sudden in Marchof 1964 at 57 years of age. I believe that he diedbefore having the opportunity to read the proofs for the second printing. This version was completed byhis graduate students at Princeton, including DavidFreedman. There was a very negative review of Wilksby Hoeffding [20]. Hoeffding never got emotional,but you can see that after a while in this long reviewhe had lost patience. Hoeffding was super consciousof the fact that parametrization was not the be alland the end all in statistics. I feel badly about mynegative findings and the Hoeffding review; thesemust have created a lot of stress. Q. It is curious that your name causes much dif-ficulty. Referring to you as E. J. Hannan is one ofseveral instances. You are James Hanaan in the bib-liography of a Peyton Young’s [37] book. You areJames Hanna in Kolata’s 2006
New York Times ar-ticle [22].You seemed to be at your MSU office most everyday of the week, even after retirement in 2002. Howmany days of the year were you not at the office? A. I did use to watch football on the weekends andon those days not come to the office. I eventuallyquit watching football since, though interesting, itwas not useful. This was probably sometime in the1960s. Q. We recall a few times when you were impatientat faculty meetings. A. In the early history we had Katz, Rubin andKallianpur on the faculty, persons with strong per-sonalities. However, there are always times whenunanimity is not available or possible.
Fig. 11.
Jim, 2005.
CONVERSATION WITH JAMES HANNAN Fig. 10.
Fig. 12.
Michigan State University Department of Mathe-matics, 1955. Bottom row: On left—Sutherland Frame. Sec-ond row: 2 from left—Leo Katz, 3 from left—Ken Arnold. Toprow: 2 from left—Jim Hannan. Q. Until recently you were heavily into exerciseand kept a number of us busy as workout partners.When did you get into this routine? A. Probably after I quit smoking in the late 1960s.I was really hooked on cigarettes and coffee at thetime. I quit coffee a month ahead of quitting smok-ing. I found it harder to quit coffee. To control weight, I also quit my habit of having a large bowl of icecream each evening. Q. We observed that you would always attemptto surpass your workout partners in regard to calo-rie burn and endurance. You were usually successfulregardless of the difference in ages. However, youfailed to top Marianne Huebner when she stood onher head for an extended period. A. I was very impressed. Q. You were not much for travel to meetings. A. I did take two leaves to the west coast, and Iusually went to Ann Arbor for the joint colloquia. Idid go to New York City for IMS Meetings in 1971.That was about it for travel. Q. Even after retirement you seem to be spendinga lot of time in the department. How do you spendtime now? A. I continue to study and work. I spent a lot oftime carefully studying the monograph on repeatedgames by Mertens, Sorin and Zamir [26]. Rustichini[30] shows that some of my results can be obtainedvia a result in this monograph. A much stronger con-clusion is possible with a weaker and easier versionof the result in MSZ. I am in the process of final-izing this. Often I start on a paper and look up areference. I find the reference interesting and followup on a reference to the reference. Thus, I may strayfar away from where I started. D. GILLILAND AND R. V. RAMAMOORTHI
REFERENCES [1]
Blackwell, D. (1956). An analog of the minimax the-orem for vector payoffs.
Pacific J. Math. Blackwell, D. (1956). Controlled random walks. In
Proceedings of the International Congress of Mathe-maticians, 1954, Amsterdam, Vol. III
Datta, S. (1991). Asymptotic optimality of Bayes com-pound estimators in compact exponential families.
Ann. Statist. Datta, S. (1991). On the consistency of posterior mix-tures and its applications.
Ann. Statist. Efron, B. and
Morris, C. (1972). Limiting the riskof Bayes and empirical Bayes estimators. II. Theempirical Bayes case.
J. Amer. Statist. Assoc. Fabian, V. and
Hannan, J. (1985).
Introduction toProbability and Mathematical Statistics . Wiley, NewYork. MR0790495[7]
Feder, M., Merhav, N. and
Gutman, M. (1992).Universal prediction of individual sequences.
IEEETrans. Inform. Theory Foster, D. P. and
Vohra, R. V. (1993). A random-ization rule for selecting forecasters.
Operations Re-search Gilliland, D. C. and
Hannan, J. (1986). The finitestate compound decision problem, equivariance andrestricted risk components. In
Adaptive StatisticalProcedures and Related Topics
Gilliland, D. C., Hannan, J. and
Huang, J. S. (1976). Asymptotic solutions to the two state com-ponent compound decision problem, Bayes versusdiffuse priors on proportions.
Ann. Statist. Gilliland, D. C. and
Hannan, J. F. (1969). On anextended compound decision problem.
Ann. Math.Statist. Hannan, J. (1960). Consistency of maximum likelihoodestimation of discrete distributions. In
Contribu-tions to Probability and Statistics
Hannan, J. F. and
Van Ryzin, J. R. (1965). Rate ofconvergence in the compound decision problem fortwo completely specified distributions.
Ann. Math.Statist. Hannan, J. (1956). The dynamic statistical decisionproblem when the component involves a finite num-ber, m , of distributions (abstract). Ann. Math.Statist. Hannan, J. (1957). Approximation to Bayes risk inrepeated play. In
Contributions to the Theory ofGames, vol. 3 . Annals of Mathematics Studies Hannan, J. and
Huang, J. S. (1972). A stabilityof symmetrization of product measures with fewdistinct factors.
Ann. Math. Statist. Hannan, J. F. and
Robbins, H. (1955). Asymptoticsolutions of the compound decision problem fortwo completely specified distributions.
Ann. Math.Statist. Hannan, J. F. (1953). Asymptotic solutions of com-pound decision problems. Ph.D. thesis, Univ. NorthCarolina.[19]
Hart, S. and
Mas-Colell, A. (2001). A general classof adaptive strategies.
J. Econom. Theory Hoeffding, W. (1962). Book review of Wilks, math-ematical statistics.
Ann. Math. Statist. James, W. and
Stein, C. (1961). Estimation withquadratic loss. In
Proc. Fourth Berkeley Sympos.Math. Statist. and Prob., Vol. I
Kolata, G. (2006). Pity the scientist who discovers thediscovered.
New York Times , Feb 5.[23]
Majumdar, S. (2007). Uniform L posterior consistencyin compact Gaussian shift experiments. J. Statist.Plann. Inference
Majumdar, S., Gilliland, D. and
Hannan, J. (1999).Bounds for robust maximum likelihood and poste-rior consistency in compound mixture state exper-iments.
Statist. Probab. Lett. Mashayekhi, M. (1993). On equivariance and the com-pound decision problem.
Ann. Statist. Mertens, J. F., Sorin, S. and
Zamir, S. (1994). Re-peated games. Discussion Paper 9420-9421-9422,CORE.[27]
Robbins, H. (1951). Asymptotically subminimax solu-tions of compound statistical decision problems.In
Proc. Second Berkeley Sympos. Math. Statist.Probab.
Robbins, H. (1956). An empirical Bayes approach tostatistics. In
Proc. Third Berkeley Sympos. Math.Statist. Probab. Robinson, J. (1951). An iterative method of solving agame.
Ann. of Math. (2) Rustichini, A. (1999). Minimizing regret: The generalcase.
Games Econom. Behav. Stein, C. (1956). Inadmissibility of the usual estima-tor for the mean of a multivariate normal distribu-tion. In
Proc. Third Berkeley Sympos. Math. Statist.Probab.
Van Ryzin, J. (1966). The sequential compound decisionproblem with m × n finite loss matrix. Ann. Math.Statist. Van Ryzin, J. R. (1966). The compound decision prob-lem with m × n finite loss matrix. Ann. Math.Statist. [34] Vardeman, S. B. (1975). O ( N / ) convergence in thefinite state restricted risk compnent sequence com-pound decision problems. Ph.D. thesis, MichiganState Univ.[35] Vardeman, S. B. (1982). Approximation to minimum k -extended Bayes risk in sequences of finite state de-cision problems and games. Bull. Inst. Math. Acad.Sinica Wilks, S. S. (1962).
Mathematical Statistics . Wiley,New York. MR0144404[37]
Young, H. P. (2004).
Strategic Learning and Its Limits .Oxford Univ. Press.[38]
Zhang, C.-H. (2003). Compound decision theory andempirical Bayes methods.
Ann. Statist.31