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Stalisticallnference Second fdition Casella George Roger l. Berger DUXBURY ADVANC ED SERIE S

01KONOMlKO nANEniITHMIO AeHNON BIBAloeHKH tao. ':fQ�� Ap. 5)q.:5 Inference Ta�. qs Statistical Second Edition George Casella University of Florida Roger L. Berger North Carolina State University DUXBURY • LEARNING THOMSON • Canada Australia • Mexico • Singapore • Spain • United Kingdom • United States

DUXBURY ! ; n-IOMSON LEARNING t.('·;ti{:)·""';1 \:jl:' • � to"� � t:. ¢ �� t ! Sponsoring Edi1;" __ .. <�. /.: / ". L,.. ", ." ': . .'" v'" ... �. ; .. ' . , ............. �."'� Cataloging-in-P -:;;6tfcation Library of Congress Data 10 9 8 7 6 5 4 3 2 1 Printed Casella, George. Statistical inference / George Casella, Roger L. Berger.-2nd ed. p. cm. ISBN 0-534-24312-6 Includes bibliographical 1. Mathematical statistics. 2. Probabilities . I. Berger II .. Title. and indexes. references I Roger L. QA216.C31 2001 519.5-dc21 2001025794

To A nne and Vicki

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Preface to the Second Edition Although perhaps Dead sentiment, "What a long, strange Sir Arthur Conan Doyle is responsible the best description can be of the life of this book trip it's been." for most of the quotes attributed in this book, to the Grateful six years with questions started about Plans for the second the answers struggled passed, clearer. We see tbe trend moving rithmic solutions of importance more important. But the manner more complex of mathematics edition about what to add and what to as the flow of the discipline away from elegant and practical indeed, we in which they are applied proofs of special cases to algo cases. This does not the have found that these have undermine become ago, and for a long time delete. Thankfully, as time of statistics became is changing. and rigor; clearer became For those familiar with the first edition, we can summarize succinctly we has been greatly expanded and simulation the changes into its own (see Section 5.5 and has , some material in Chapters 3-11 for clarity. with respect to computer algebra Appendix Discussion of asymptotic methods on computing ); coverage algebra or added (for example, bootstr as follows. chapter. There is more emphasis the computer been expanded logistic regression and robust We have de-emphasized the more and decision specialized and have restructured First, that we want to note. theory, There are two things although of the more applicable techniques ); and there are many new Miscellanea and Exercises. the EM algorithm, p-values apping, theoretica l topics, such as equivari ance system The first are numbered 7.2.5 and Theorem that facilitates finding who does not share that belief. that they are becoming we believe programs, tools, increasingly valuable we did not want to force them on the instructor Thus, the treatment usive" is "unobtr in that it appears only in an appendix, with some hints throughout the book where it may be useful. Second, we have changed things. the numbering to one Now theorems, lemmas, for example, together; examples, and definitions Definition 7.2.4 is followed precedes 10.1.3 10.1.4. only minor changes. We reordered some ma have been split), added some new Chapter 5 has also been re back, and a new section on of invariance, which was reduced and (mostly and includes minor editing terial examples ordered generating in Chapters Chapter new exercises on the EM algorithm. by Example four chapters (in particular, and exercises, , witb the random variables 7-9 of the first edition, ). Chapter updating. being moved further The previous has been int.o the addition a new section and updating, only minor editing and updated, and did some general 7 has been Chapter the inequalities 6, which otherwise 8 has also received and identities convergence section have received has received expanded coverage greatly Example added. and of incorporated

- '-f .-MIJIA\'¥ )""'111 ,.....".,.- ,;,\� \: '��s� ��e\\T" sjl��?'4 p-values. In Chapter ." I PREFACE TO THE SECOND EDITION "guaranteeing an interval" was in Chapter 10 of the first edition and small sections and interval (h8.vJn��hat the rrrateihirihat duced, testing, 10 is entirely Chapter inference, including robust strapping, (which and linear regression Unfortunately, tion). coverage space reasons. 12 covers on robust material After teaching Chapter and logistic estimators, score tests, was covered of randomized regression regression. on loss function what can be covered possible to cover the following in one year: 9 we now put more emphasis "pivoting theory) (decision on pivot the cdf"). Also, was merely ing has been re hypothesis estimation have been new and attempts of point optimality added to the appropriate to layout the fundamentals the delta method, consistency and asymptotic estimation, chapters. of large sample normality, oneway ANOVA in the first edi for new and contains boot etc. Chapter in two different block designs 11 is classic chapters has been eliminated with errors-in- variables from the first edition in a one-year for a number of years, we know (approximately) course. From the second edition, it should be Chapter Chapter Chapter Chapter Chapter 1: Sections 2: Sections 3: Sections 4: Sections 5: Sections 1-7 Chapter 1-3 Chapter 1-6 Chapter 1-7 Chapter 1-6 Chapter 6: Sections 7: Sections 8: Sections 1-3 9: Sections 10: Sections 1-3 1, 3, 4 1-3 1-3 that begin the course with some probability background can cover more ma Classes terial from the later chapter s. Finally, it is almost impossible to thank all of the people who have contributed (and help us correct and colleagues in in who took the time to the mistakes A number of people made key suggestions in presentation. Sometimes reviews. these suggestions Some were so long ago that were just may have forgotten, but we haven't. So thanks to Arthur Cohen, Sir changes To all of our students, a reality friends, we thank you. some way to making the second edition the first edition). send us a note or an e-mail, that led to substantial short notes or comments, their authors David Cox, Steve Samuels, Jay Beder, who has knows the first edition possibly class, comments sent us numerous better and corrections This book has seen a number of editors. and some were longer Rob Strawderman who are sending doing a first suggested mid-1990s who constantly responsible for and marketed encouraged this book is our first editor, the first edition. John. second us. Perhaps Thanks, edition, the one person John Kimmel, and Tom Wehrly. We also owe much to over the years and and suggestions comments than we do, and to Michael Perlman and his even as we write this. We thank Alex Kugashev, who in the and our editor, Carolyn Crockett, (other than us) who is most who encouraged, published, George Roger Casella L. Berger

Preface to the First Edition a textbook, one (or that you are writing asked. The first is "Why are you writing When someone discovers tions will be "How is your book different from out there?" a book because to answer. You are writing you are available texts. question in a few sentences question only out of politenes work. doesn't is The first question not entirely to answer. The answer is fairly easy satisfied with the can't be put (who may be asking the quick and witty. so, in order not to bore your audience to say something both) of two ques s), you try The second is harder what's a book?" and the second It usually to build theoretical statistics (as different from mathe The purpo se of this book is from the first principl themes, et c., evolve matical statistics) proofs, ideas, the basics niques, consequences how well it would work. The final judgment reader. of probability, and concepts definitions, of previous that are statistica When this we develop the concepts. through es of probability theory. arguments. Logical development, Thus, starting of statistical inference statistical theory using tech from l and are natural endeavor was started, of our success is, of course, we were not sure left to the extensions and The book is intended a field where a statistics calculus. essential course (Some familiarity .) The book in statistics. for first-year graduate concentration majoring students is desirable. manipulati or in is one year of The prerequisite ons would be useful, but is not introductory in statistics can be used for a two-semester, or three-quarter, with matrix The first four chapters cover basics that are later necessary. many fun of probability theory and introduce al chapters. and can be the starting statistic and statistics) Chapters probability 5 and 6 are the first 5 is transitional (between in statistical for students theory detailing three with some probabilit princip how these principles are important les (sufficiency, in modeling statistical y backgrou nd. like ) and showing unique, will cover this chapter in some time here. In particular, them, are fundamental Along with the sufficiency to total the central core detail, although the likelihood principle, statistical of statistical inference, we strongly and invariance principles these principl es, and the understanding. estimation (point recom 7-9 represent ) and hypothesis Chapters and interval into methods of finding these techniques. appropriate and evaluating Finding testing. A major statistical feature of these chapters techniques and methods is the division of evaluating are of interest to both the theorist and the damentals Chapter point for a course 6 is somewhat Chapter lihood, and invariance data. Not all instructors mend spending are treated thinking in detail. behind

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