Stephen M. Stigler

The Journals of Economics

We examine the principal journals of economics, with particular attention to the communication between journals, as reflected by the network of interjournal citations during 1987-90, and the changes over the past century in the characteristics of the authors and the techniques they have used. The numerical results, and those of the statistical modeling of these results, reinforce the importance of economic theory as an exporter of intellectual influence to applied economics. The study includes an examination of the degree of specialization among different subfields of economics. A statistical model is presented for measuring the flow of intellectual influence (as measured by citations) in terms of simple univariate scores.

Optimal Experimental Design for Polynomial Regression

Abstract The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and discussed. Use of these criteria is illustrated by a detailed discussion of the case that the regression function can be assumed approximately linear. These criteria, which can be considered as compromises between the incompatible goals of inference about the regression function under an assumed model and of checking the models adequacy, are found to yield designs superior in certain respects to others which have been proposed to deal with this problem, including minimum bias designs.

Regression towards the mean, historically considered

The simple yet subtle concept of regression towards the mean is reviewed historically. Verbal, geometric, and mathematical expressions of the concept date to the discoverer of the concept, Francis Galton. That discovery and subsequent understanding (and misunderstanding) of the concept are surveyed.

Fisher and the 5% Level

Surely R. A. Fisher played a major role in the canonization of the 5% level as a criterion for statistical significance, although broader social factors were involved. Fisher needed tables for his 1925 book and, evidently, Karl Pearson would not permit the free reproduction of the Biometrika tables, so Fisher computed his own. Fisher found it convenient to table values in the extremes for levels such as 10%, 5%, 2%, 1%—roughly halving the level with each step. One simple explanation for the format he selected lies in the fact that the book introduced “analysis of variance,” or ANOVA. For most readers, this would be their fi rst exposure to ANOVA, and Fisher needed a way to make the new test accessible— essentially the F-test, although he preferred to work in terms of z = log(F). The table here was entirely novel, requiring entry via two parameters: the numerator and denominator degrees of freedom (df). It would have been impractical to provide a full table of the distribution for each pair of values: With the 10 levels of both dfs he wished to include, 100 tables would have been required if he gave the same level of detail he gave for his normal distribution table, or 10 tables if he gave the reduced level of detail that Gosset gave in his 1908 table for the t-distributions. So, Fisher initially settled on only giving one table for the 5% point. Once that was decided, it is not implausible that Fisher chose (in a book for practical workers) to make the other tables conform to that same simple format. This was not a huge task, and it had the bonus of casting all assessments of signifi cance in the same accessible form. The fi rst edition (1925) of Fisher’s book Statistical Methods for Research Workers had six tables:

Simon Newcomb, Percy Daniell, and the History of Robust Estimation 1885–1920

Abstract This article reviews some of the history of robust estimation, emphasizing the period 1885–1920 and the work of Newcomb, Edgeworth, Sheppard, and Daniell. Particular attention is paid to lines of development which have excited recent interest, including linear functions of order statistics and mixtures of normal densities as models for heavy-tailed populations.

W. Edwards Deming

Long recognized as a leading proponent of statistical sampling and approaches to quality improvement, Deming led major efforts to bring statistical approaches and methods to bear on problems in government, science and industry.

Fractional Order Statistics, with Applications

Abstract Based upon Fergusons Dirichlet process, we introduce an order-statistic process, a technical device which may be viewed as defining a continuum of fractional order statistics for any sample size. The order-statistic process provides an alternative to the quantile function essentially based on stochastic rather than linear interpolation. Its use in large-sample theory is suggested, and a simple proof is given that the order-statistic process, suitably normalized, converges to a Gaussian process. Applications to small-sample theory and to the passage-time distribution of Yule processes are also considered, and a class of censored-data problems is related to mixtures of these processes.

Statistical Properties of the Buddy System

The utilization of space and the running speed of the buddy system are considered Equations are derived that give various statistical properties of the buddy system. For the bottom level with Poisson requests and exponential service times the expected amount of space wasted by pairing full cells with empty cells is about 0.513 <subscrpt><italic>&rgr;</italic></subscrpt><supscrpt>1/2</supscrpt> and the mean time between requests from the bottom level to the next level is about 1.880 <subscrpt><italic>&rgr;</italic></subscrpt><supscrpt>1/2</supscrpt> λ<supscrpt>-1</supscrpt>, where <italic>&rgr;</italic> is the mean number of blocks in use on the bottom level and λ<supscrpt>-1</supscrpt> is the mean time between requests for blocks on the bottom level. The results of a number of simulations of the buddy system are also given and compared with the analytical studies.

The Kelvin dictum and social science: an excursion into the history of an idea.

Lord Kelvins dictum on the importance of measurement in science is frequently quoted (and more frequently misquoted). One version is to be found on the facade of the University of Chicagos Social Science Research Building. An impromptu excursion into the history and uses of this inscription sheds light on the roles of measurement and quotation in scholarship.

Fisher in 1921

Ronald A. Fishers 1921 article on mathematical statistics (sub mitted and read in 1921; published in 1922) was arguably the most influential article on that subject in the twentieth century, yet up to that time Fisher was primarily occupied with other pursuits. A number of previously published documents are examined in a new light to argue that the origin of that work owes a considerable (and unacknowledged) debt to a challenge issued in 1916 by Karl Pearson.