Mathematical Statistics: Exercises and Solutions [Paperback]

Jun Shao (Author)

Book Description

Publication Date: June 30, 2005 | ISBN-10: 0387249702 | ISBN-13: 978-0387249704 | Edition: 1

The exercises are grouped into seven chapters with titles matching those in the author's Mathematical Statistics. Can also be used as a stand-alone because exercises and solutions are comprehensible independently of their source, and notation and terminology are explained in the front of the book. Suitable for self-study for a statistics Ph.D. qualifying exam.

Editorial Reviews

Review

From the reviews: "This book contains 400 exercises with their detailed solutions. … It has an extensive list of notations and terminologies and can be used as a stand-alone book. This book will be very useful to Statistics students studying towards an M.Sc or a Ph.D. degree, by helping them to develop problem solving skills … . It will be useful to their teachers as a source of solved exercises. The list of 26 distributions given at the beginning will also be useful for ready reference.” (Mausumi Bose, Sankhya, Vol. 67 (4), 2005) "The exercise book accompanies an excellent text book for a graduate course in mathematical statistics ... and is an excellent support for the book. The exercise book is excellent by itself also: a challenging collection of problems in mathematical statistics. … Using both however, the textbook and the exercise book, the mathematical statistician will enjoy the wealth of interesting problems." (Götz Uebe, Allgemeines Statistisches Archiv, Issue 2, 2005) "This book consists of solutions to 400 exercises in the general theory of mathematical statistics … . The solutions of the exercises are thorough and explain the different steps in great detail. These solutions will certainly help students to a better understanding of the many complicated issues in the theory. This book is thus a valuable contribution to the teaching materials currently available." (Jon Stene, Mathematical Reviews, Issue 2006 b) "This collection consists of 400 exercises and their solutions. Most of the exercises (over 95%) are introduced in the cited textbook. … The collection is a stand-alone book. It is written very rigorously and solutions are presented in detail. It can be recommended as a source of solved problems for teachers and students of advanced mathematical statistics." (EMS Newsletter, June, 2006)

From the Back Cover

This book consists of four hundred exercises in mathematical statistics and their solutions, over 95% of which are in the author's Mathematical Statistics, Second Edition (Springer, 2003). For students preparing for work on a Ph.D. degree in statistics and instructors of mathematical statistics courses, this useful book provides solutions to train students for their research ability in mathematical statistics and presents many additional results and examples that complement any text in mathematical statistics. To develop problem-solving skills, two solutions and/or notes of brief discussions accompany a few exercises. The exercises are grouped into seven chapters with titles matching those in the author's Mathematical Statistics. On the other hand, the book is stand-alone because exercises and solutions are comprehensible independently of their source, and notation and terminology are explained in the front of the book. Readers are assumed to have a good knowledge in advanced calculus. A course in real analysis or measure theory is highly recommended. If this book is used with a statistics textbook that does not include probability theory, then knowledge in measure-theoretic probability theory is required. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison.

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Product Details

• Paperback: 388 pages
• Publisher: Springer; 1 edition (June 30, 2005)
• Language: English
• ISBN-10: 0387249702
• ISBN-13: 978-0387249704
• Product Dimensions: 9.2 x 6.1 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #926,152 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

34 of 37 people found the following review helpful:

5.0 out of 5 stars a measure-theoretic based introduction to statistics, September 30, 2002

By 

Todd Ebert (Long Beach California) - See all my reviews

This review is from: Mathematical Statistics (Springer Series in Statistics) (Hardcover)

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.

19 of 22 people found the following review helpful:

5.0 out of 5 stars Great book, not for kids, January 12, 2004

By A Customer

This review is from: Mathematical Statistics (Hardcover)

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.

14 of 16 people found the following review helpful:

5.0 out of 5 stars Worth the time reading, December 7, 2003

By 

GM (Campbell, CA USA) - See all my reviews

This review is from: Mathematical Statistics (Hardcover)

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.