Product Description

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.

Product Details

• Amazon Sales Rank: #754886 in Books
• Published on: 2007-10-05
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 520 pages

Review

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)

About the Author

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

Customer Reviews

a measure-theoretic based introduction to statistics
This book has all the ingredients of what in my opinion constitutes an excellent mathematics text: rigorous, concise,
self-contained, clear, and taking an abstract point of view. Note however that, due to the latter ingredient, the author studies statistics using a measure-theoretic approach; and thus I highly recommend that a potential reader first study measure theory as a prerequisite. The first chapter reviews the basics of measure theory, but it may seem too giant a first step for some readers.

The first two chapters of the book give a nice overview of probability and statistics, while the remaining chapters expand on three fundamental areas of statistical inference: estimation (both parametric and nonparametric), hypothesis tests, and confidence sets). And I must admit that I'm very impressed with the author! For if a textbook is a reflection of what an author knows about some subject, then Shao represents a treasure trove of knowledge that is so eloquently shared in this book. Anyone serious about doing graduate-level reasearch in statistics should invest a year of studying this book. But be forwarned that most likely one will find this, due to the onslaught of measure theoretic analysis, one of the more challenging books to makes its way on the book shelf. For those who cannot stomach so much analysis, but would like to at least understand the gist of statistics, I recommend Roussas's book of the same title. It is calculus-based and makes some simplifying assumptions (e.g. continuous or discrete) about the distributions, which helps make the math digest easier.

Great book, not for kids
Don't waste your time: this is a rigorous book on mathematical statistics, done right, for mathematically mature readers.

If you want a plug and chug manual, buy something else. If you want precision and rigor, buy this.

Worth the time reading
Very readible, precise and concise treatment of statistics. Requires mathematical maturity. Although it doesn't require a background in measure theory, some familiarity (or willingness to learn) would be really helpful (Ch. 1 provides an overview of measure-theoretic probability). I read the first half of it in a PhD level statics class. I found its approach refreshing after taking an engineering oriented senior level/grad statistics class. I still frequently consult it.