Mathematical statistics

Jun Shao0387953825, 9780387953823

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are usefulin statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to the classical results that are typically covered in a textbook of a similar level, this book introduces some topics in modern statistical theory that have been developed in recent years, such as Markov chain Monte Carlo, quasi-likelihoods, empirical likelihoods, statistical functionals, generalized estimation equations, the jackknife, and the bootstrap. In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics. Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, conditional independence, Markov chains, martingales, Edgeworth and Cornish-Fisher expansions, and proofs to many key theorems such as the dominated convergence theorem, monotone convergence theorem, uniqueness theorem, continuity theorem, law of large numbers, and central limit theorem. A new section in Chapter 5 introduces semiparametric models, and a number of new exercises were added to each chapter. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison. Also available: Jun Shao and Dongsheng Tu, The Jackknife and Bootstrap, Springer-Verlag New York, Inc., 1995, Cloth, 536 pp., 0-387-94515-6.

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Table of contents :
41gnEIQ1jvL……Page 1
front-matter……Page 2
01Probability Theory……Page 17
02Fundamentals of Statistics……Page 107
03Unbiased Estimation……Page 177
04Estimation in Parametric Models……Page 247
05Estimation in Nonparametric Models……Page 335
06Hypothesis Tests……Page 409
07Confidence Sets……Page 487
back-matter……Page 559