Mathematical Statistics

ISBN-13: 9781441929785 / Angielski / Miękka / 2010 / 592 str.

Jun Shao

Opis

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. 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.

Recenzje

From the reviews of the second edition:

"The second edition of Mathematical Statistics continues to hold its identity among many other available books on mathematical statistics...The revised and updated version remains of high quality, and I recommend it for use as a text or reference book in a graduate statistics program." Journal of the American Statistical Association, September 2004

"The first edition of this book was published in 1999 ... . The main changes include addition of new material in Chapter 1, addition and deletion of a number of exercises, addition of two new sub-sections ... . The book remains valuable to instructors and graduate students of traditional mathematical statistics courses, specially for its large collection of problems and for its rigourous presentation." (Arup Bose, Sankhya: The Indian Journal of Statistics, Vol. 65 (3), 2003)

"This book is intended for an advanced postgraduate course in Mathematical Statistics, offered in a mathematically rigorous fashion. ... in order to get to grips with rigorous mathematical statistics, this is an ideal book. Also, as a reference book, it is ideally suited. ... Two particularly attractive features of the book are the large number of exercises at the end of each chapter - well over a hundred in each chapter, and the fact that asymptotic theory is studied throughout the book ... ." (Tertius de Wet, SASJ - South African Statistical Journal, March, 2004)

Spis treści

Probability Theory * Fundamentals of Statistics * Unbiased Estimation * Estimation in Parametric Models * Estimation in Nonparametric Models * Hypothesis Tests * Confidence Sets

O autorze

Jun Shao is Professor of Statistics at the University of Wisconsin, Madison.