Theoretical Statistics: Topics for a Core Course

ISBN-13: 9781461426707 / Angielski / Miękka / 2012 / 538 str.

Robert W. Keener

Opis

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.

Recenzje

From the reviews:

"The book is innovative in the presentation and in mashing the traditional material with modern topics. The presentation shows a great mastery of the subject. ... recommended to someone who has a working knowledge of statistics and would like to learn more about the theory. ... As a text for a course, the book is versatile. ... The mathematical level is correct for a first year graduate course and may be appropriate at some universities for courses whose primary audience is seniors." (Stephan Morgenthaler, Mathematical Reviews, Issue 2011 m)

"This volume provides an excellent course in the mathematical theory underlying statistical ideas and methods, for advanced ... students. The amount of material covered is indicated by the fact that it evolved from a three-semester sequence of courses given by the author. Its suitability as a course text is materially aided by very extensive exercises, along with solutions to selected exercises. Anyone who works through this book will end up with a first class understanding of the mathematical ideas underlying modern statistical concepts and methods." (David J. Hand, International Statistical Review, Vol. 80 (1), 2012)

"The book extensively covers classic and modern topics of theoretical statistics in a rigorous manner. ... The book provides more than 400 exercise problems. ... There are many books on statistical theory but very few have such great breadth and scope of materials as this book. ... the book is well written and it is a great addition to the collection of books on statistical theory. ... It will serve well both as a textbook and a reference book." (Xianggui Qu, Technometrics, Vol. 53 (3), August, 2011)

Spis treści

Probability and Measure.- Exponential Families.- Risk, Sufficiency, Completeness, and Ancillarity.- Unbiased Estimation.- Curved Exponential Families.- Conditional Distributions.- Bayesian Estimation.- Large-Sample Theory.- Estimating Equations and Maximum Likelihood.- Equivariant Estimation.- Empirical Bayes and Shrinkage Estimators.- Hypothesis Testing.- Optimal Tests in Higher Dimensions.- General Linear Model.- Bayesian Inference: Modeling and Computation.- Asymptotic Optimality1.- Large-Sample Theory for Likelihood Ratio Tests.- Nonparametric Regression.- Bootstrap Methods.- Sequential Methods.

O autorze

Robert Keener is Professor of Statistics at the University of Michigan and a fellow of the Institute of Mathematical Statistics.

Blurb

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.