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Mathematical Statistics: Springer Texts in Statistics

Autor Jun Shao
en Limba Engleză Paperback – dec 2010
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 useful in 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 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.
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Specificații

ISBN-13: 9781441929785
ISBN-10: 1441929789
Pagini: 608
Ilustrații: XVI, 592 p.
Dimensiuni: 155 x 235 x 32 mm
Greutate: 0.84 kg
Ediția:Softcover reprint of hardcover 2nd ed. 2003
Editura: Springer
Colecția Springer
Seria Springer Texts in Statistics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

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

Recenzii

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)

Caracteristici

Includes supplementary material: sn.pub/extras

Descriere

Descriere de la o altă ediție sau format:
Since the publication of my book Mathematical Statistics (Shao, 2003), I have been asked many times for a solution manual to the exercises in my book. Without doubt, exercises form an important part of a textbook on mathematical statistics, not only in training students for their research ability in mathematical statistics but also in presenting many additional results as complementary material to the main text. Written solutions to these exercises are important for students who initially do not have the skills in solving these exercises completely and are very helpful for instructors of a mathematical statistics course (whether or not my book Mathematical Statistics is used as the textbook) in providing answers to students as well as ?nding additional examples to the main text. Mo- vatedbythisandencouragedbysomeofmycolleaguesandSpringer-Verlag editor John Kimmel, I have completed this book,Mathematical Statistics: Exercises and Solutions. This book consists of solutions to 400 exercises, over 95% of which are in my bookMathematical Statistics. Many of them are standard exercises that also appear in other textbooks listed in the references. It is only a partial solution manual to Mathematical Statistics (which contains over 900exercises).

Notă biografică

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

Textul de pe ultima copertă

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.