โ Scribed by Robert W. Keener (auth.)
No coin nor oath required. For personal study only.
Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix. Robert Keener is Professor of Statistics at the University of Michigan and a fellow of the Institute of Mathematical Statistics.
Front Matter....Pages i-xvii
Probability and Measure....Pages 1-24
Exponential Families....Pages 25-38
Risk, Sufficiency, Completeness, and Ancillarity....Pages 39-59
Unbiased Estimation....Pages 61-83
Curved Exponential Families....Pages 85-99
Conditional Distributions....Pages 101-113
Bayesian Estimation....Pages 115-127
Large-Sample Theory....Pages 129-149
Estimating Equations and Maximum Likelihood....Pages 151-194
Equivariant Estimation....Pages 195-203
Empirical Bayes and Shrinkage Estimators....Pages 205-218
Hypothesis Testing....Pages 219-253
Optimal Tests in Higher Dimensions....Pages 255-267
General Linear Model....Pages 269-299
Bayesian Inference: Modeling and Computation....Pages 301-318
Asymptotic Optimality 1 ....Pages 319-342
Large-Sample Theory for Likelihood Ratio Tests....Pages 343-366
Nonparametric Regression....Pages 367-390
Bootstrap Methods....Pages 391-403
Sequential Methods....Pages 405-430
Back Matter....Pages 431-538
Statistical Theory and Methods
๐ SIMILAR VOLUMES
obtained thanks to https://t.me/HermitianSociety
<p><p>This book highlights the latest research findings from the 46th International Meeting of the Italian Statistical Society (SIS) in Rome, during which both methodological and applied statistical research was discussed. This selection of fully peer-reviewed papers, originally presented at the mee