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Mathematical Statistics: Exercises and Solutions
Jun Shao
Mathematical
Statistics:
Exercises and
Solutions
82234036.001.png
Jun Shao
Department of Statistics
University of Wisconsin
Madison, WI 52706
USA
shao@stat.wisc.edu
Library of Congress Control Number: 2005923578
ISBN-10: 0-387-24970-2
Printed on acid-free paper.
ISBN-13: 978-0387-24970-4
© 2005 Springer Science + Business Media, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science + Business Media, Inc., 233 Spring Street,
New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly
analysis. Use in connection with any form of information storage and retrieval, electronic adap-
tation, computer software, or by similar or dissimilar methodology now known or hereafter de-
veloped is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even
if they are not identified as such, is not to be taken as an expression of opinion as to whether
or not they are subject to proprietary rights.
Printed in the United States of America.
(EB)
987654321
springeronline.com
To My Parent s
Preface
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 finding additional examples to the main text. Moti-
vated by this and encouraged by some of my colleagues and Springer-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 book Mathematical 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
900 exercises). However, the types of exercise in Mathematical Statistics not
selected in the current book are (1) exercises that are routine (each exercise
selected in this book has a certain degree of di culty), (2) exercises similar
to one or several exercises selected in the current book, and (3) exercises for
advanced materials that are often not included in a mathematical statistics
course for first-year Ph.D. students in statistics (e.g., Edgeworth expan-
sions and second-order accuracy of confidence sets, empirical likelihoods,
statistical functionals, generalized linear models, nonparametric tests, and
theory for the bootstrap and jackknife, etc.). On the other hand, this is
a stand-alone book, since exercises and solutions are comprehensible
independently of their source for likely readers. To help readers not
using this book together with Mathematical Statistics , lists of notation,
terminology, and some probability distributions are given in the front of
the book.
vii

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