Dimitris Karlis

Simulation from the bessel distribution with applications

The Bessel distribution, introduced recently by Yuan and Kalbfleisch (Ann. Inst. Math. Statist., 2000), can be useful in many applications. In particular, this distribution appears in two Bayesian estimation problems, namely, estimation of the noncentrality parameter of a noncentral chi-square distribution and of the parameters of Downtons bivariate exponential distribution. Implementation of Markov chain Monte Carlo algorithms requires generation of observations from the Bessel distribution. In this paper we propose and compare exact simulation schemes generating Bessel variates based on certain properties of the distribution as well as the rejection method.

Confidence intervals of the hazard rate function for discrete distributions using mixtures

The statistical models and methods for lifetime data mainly deal with continuous nonnegative lifetime distributions. However, discrete lifetimes arise in various common situations where either the clock time is not the best scale for measuring lifetime or the lifetime is measured discretely. In most settings involving lifetime data, the population under study is not homogenous. Mixture models, in particular mixtures of discrete distributions, provide a natural answer to this problem. Nonparametric mixtures of power series distributions are considered, as for instance nonparametric mixtures of Poisson laws or nonparametric mixtures of geometric laws. The mixing distribution is estimated by nonparametric maximum likelihood (NPML). Next, the NPML estimator is used to build estimates and confidence intervals for the hazard rate function of the discrete lifetime distribution. To improve the performance of the confidence intervals, a bootstrap procedure is considered where the estimated mixture is used for resampling. Various bootstrap confidence intervals are investigated and compared to the confidence intervals obtained directly from the NPML estimates.

Book Review: Regression analysis by example, 3rd edition

In this new edition the authors offer a wide range of topics that occur in standard regression models. Though the researcher may face these issues frequently, in many cases they may be awkward to handle. The book provides a variety of topics that usual regression textbooks ignore or, at least, treat superx8ecially. While this book provides only a review of the basic principles of regression, it covers many other topics, mainly on problems occurring during a regression analysis. Diagnostic tools as well as methods to overcome the problems are discussed in a very efx8ecient way, balancing between practical and theoretical treatment. It is important that technical terms are explained in a simple way, making the book tractable for a wide audience. The introductory chapter mainly tries to prepare the ground for the rest of book by merely dex8ening the regression model and providing information on potential applications of the model. Chapter 2 dex8enes the simple regression model and all the classical topics (estimation, inference, goodness of x8et, predictions, etc.), while Chapter 3 treats the multiple regression case. Perhaps these are the only chapters with the usual material covered in other books. The description is short and only the basic results are reported. The remaining chapters are devoted to specialized topics of regression. Chapter 4 discusses model deviation diagnostics, including graphical tools, detection of outliers, inx8fuence robustness, etc. Chapter 5 introduces the use of qualitative predictors (dummy variables, interaction terms, seasonality terms). Chapter 6 presents transformation of variables and Chapter 7 weighted regression. Correlated errors are treated in Chapter 8, and multicollinearity problems in Chapter 9. Biased regression, including ridge regression and principal components regression, is presented in Chapter 10. The remaining two chapters treat variable selection problems (Chapter 11) and logistic regression (Chapter 12). It is odd that only logistic regression is presented from all the variants of the regression model. Throughout the book there are plenty of examples to demonstrate the ideas presented. Some of the data sets are quite famous for the purpose used (e.g., Anscombe data, the salary survey data). The examples are derived from a wide range of disciplines and present real problems. Every chapter ends with exercises for better comprehension. It is important that one can x8end a lot of diagnostic and problem-solving techniques that are rarely available together in other books. Therefore the book is very useful as a problem-solving guide to real problems. Some of the drawbacks of the book are the limited use of matrix representation of the regression model (just three pages) and the almost total omission of the more general setting of the ANOVA model as a linear model. Also there are a lot of examples not covered in enough depth to enable the reader to gain more understanding of the data. In summary, the book contains a thorough overview of diagnostic tools for regression models that are sensibly arranged and easily understood. It is not of the standard textbook form since the basic results on regression are quickly presented and the main focus is on how one can overcome the various problems occurring in real data applications. Owing to this orientation, the book needs a prior knowledge of regression, and thus it is useful for applied researchers with previous experience with regression and not so much for students or beginners.

Book Review: Models for discrete data

towards positive results in favour of the new treatment. The problem with cluster-randomized trials is that in many cases concealment may be totally impractical. Then, when there is any possibility of selection, for example, if the patient is required to consent to a known intervention determined by their place of residence, there is the possibility that certain patients may selectively decline to enter the trial so as to obtain the treatment of their choice, and this could lead to bias. Such bias can seriously jeopardize cluster-randomized trials, and ought to have been discussed. This reservation aside, an extremely good and readable book; highly recommended. Most of the chapters are sufficiently straightforward to be understood by the majority of readers familiar with clinical trial methodology, and only a limited level of statistical knowledge is assumed. However, the detailed analysis methods, although well written and essentially straightforward, will, I feel, be difficult for the clinician or none mathematician to implement without the assistance of an experienced statistician. That apart this is a highly recommended book for most readers who are in any way involved in cluster randomized trials, whether students or researchers, statisticians or clinicians.