The Statistical Analysis of Discrete Data

The Statistical Analysis of Discrete Data provides an introduction to cur rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap ply the methods in the text, to explore extensions of the material covered, and to analyze data with discrete responses. In the text examples, and in the problems, we have sought to include interesting data sets from a wide variety of fields including political science, medicine, nuclear engineering, sociology, ecology, cancer research, library science, and biology. Although there are several texts available on discrete data analysis, we felt there was a need for a book which incorporated some of the myriad recent research advances. Our motivation was to introduce the subject by emphasizing its ties to the well-known theories of linear models, experi mental design, and regression diagnostics, as well as to describe alterna tive methodologies (Bayesian, smoothing, etc. ); the latter are based on the premise that external information is available. These overriding goals, to gether with our own experiences and biases, have governed our choice of topics.

Autorentext

Thomas J. Santner is Professor Emeritus in the Department of Statistics at The Ohio State University. At Ohio State, he has served as department Chair and Director of the Department's Statistical Consulting Service. Previously, he was a professor in the School of Operations Research and Industrial Engineering at Cornell University. His research interests include the design and analysis of experiments, particularly those involving computer simulators, Bayesian inference, and the analysis of discrete response data. He is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, and is an elected ordinary member of the International Statistical Institute. He has held visiting appointments at the National Cancer Institute, the University of Washington, Ludwig Maximilians Universität (Munich, Germany), the National Institute of Statistical Science (NISS), and the Isaac Newton Institute (Cambridge, England). Brian J. Williams has been Statistician at the Los Alamos National Laboratory RAND Corporation since 2003. His research interests include experimental design, computer experiments, Bayesian inference, spatial statistics and statistical computing. Williams was named a Fellow of the American Statistical Association in 2015 and is also the recipient of the Los Alamos Achievement Award for his leadership role in the Consortium for Advanced Simulation of Light Water Reactors (CASL) Program. He holds a doctorate in statistics from The Ohio State University. William I. Notz is Professor Emeritus in the Department of Statistics at The Ohio State University. At Ohio State, he has served as acting department chair, associate dean of the College of Mathematical and Physical Sciences, and as director of the department's StatisticalConsulting Service. His research focuses on experimental designs for computer experiments and he is particularly interested in sequential strategies for selecting points at which to run a computer simulator in order to optimize some performance measure related to the objectives of the computer experiment. A Fellow of the American Statistical Association, Notz has also served as Editor of the journals Technometrics and the Journal of Statistics Education.

Klappentext

The Statistical Analysis of Discrete Data provides an up-to-date introduction to methods for analyzing discrete data. The text covers both single-sample problems and problems with structured means which can be studied via loglinear and logistic models. Standard estimation and testing formulations are joined by formulations in terms of multiple comparisons, simultaneous interval construction, and ranking and selection. Where possible, connections with linear model theory for continuous responses are exploited to emphasize the relationships between the two areas. Recent research in areas such as graphical models for contingency tabels, Bayes and related estimation for loglinear models, and diagnostics for logistic regression is presented. Problems at the end of each chapter provide opportunities to both try out methods in the text on data from a wide variety of fields and to explore extensions of the material covered. The book is intended as a textbook for researchers both in- and outside of the statistics field who encounter discrete data.

Inhalt
1 Introduction.- 2 Univariate Discrete Responses.- 3 Loglinear Models.- 4 Cross-Classified Data.- 5 Univariate Discrete Data with Covariates.- Appendix 1. Some Results from Linear Algebra.- Appendix 2. Maximization of Concave Functions.- Appendix 3. Proof of Proposition 3.3.1 (ii) and (iii).- Appendix 4. Elements of Large Sample Theory.- Problems.- References.- List of Notation.- Index to Data Sets.- Author Index.