Statistical Inference 2nd Edition

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Statistical Inference 2nd Edition
Duxbury Press An Imprint of Wadsworth Publishing Company a division of wadsworth. Inc o 1990 by Wadsworth, Inc, Belmont, California 94002 All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transcribed in any form or by any means-electronic, mechanical, photocopying, recording or otherwise--without the prior written permission of the publisher. Wadsworth Publishing Company, Belmont, California 94002 Printed in the United States of America 1098 Library of Congress Cataloging in Publication Data Casella, George Statistical inference/George Casella, Roger L. Berger ct Includes bibliographical references ISBN0-534-11958-1 1. Mathematical statistics. 2. Probabilities, I. Berger, Roger L. I. T QA276C371990 519.5-dc20 89-27287 CIP Sponsoring Editor: John Kimmel Marketing Representative: Charlie Delmar Editorial Assistant: Jenny Greenwood Production Coordinator: Joan marsh Interior Design: Vemon Boes Cover Design: Lisa Thompson Interior Illustration: Lori Heckelman Typesetting: Electronic Technical Publishing Cover Printing: Phoenix Color Corporation Printing and Binding: Arcata Graphics/Fairfield To Anne and vicki Preface When someone discovers that you are writing a textbook, one (or both) of two ques tions will be asked. The first is"Why are you writing a book? "and the second is How is your book different from what's out there? "The first question is fairly easy Lo answer. You are writing a book because you are not entirely satisfied with the available texts. The second question is harder to answer. The answer cant be put in a few sentences so, in order not to bore your audience(who may be asking the question only out of politeness), you try to say something quick and witty. It usually doesnt work The purpose of this book is to build theoretical statistics (as different from mathematical statistics) from the first principles of probability theory. Logical de velopment, proofs, ideas, themes, etc evolve through statistical arguments. Thus, starting from the basics of probability, we develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural exten- sions and consequences of previous concepts. When this endeavor was started, we were not sure how well it would work. The final judgment of our success is,of course. left to the reader The book is intended for first-year graduate students majoring in statistics or in a field where a statistics concentration is desirable. The prerequisite is one year of calculus.(Some familiarity with matrix manipulations would be useful, but is not essential. The book book can be used for a two-semester, or three-quarter, introductory course in statistics The first four chapters cover basics of probability theory and introduce many fundamentals that are later necessary. Chapters 5 and 6 are the first statistical chapters Chapter 5 is transitional (between probability and statistics) and can be the starting point for a course in statistical theory for students with some probability background Chapter 6 is somewhat unique, detailing three statistical principles(sufficiency, like- lihood, and invariance) and showing how these principles are important in modeling data. Not all instructors will cover this chapter in detail, although we strongly recom mend spending some time here. In particular, the likelihood and invariance principles are treated in detail. Along with the sufficiency principle, these principles, and the thinking behind them, are fundamental to total statistical understanding viii Preface Chapters 7-9 represent the central core of statistical inference, estimation (point and interval) and hypothesis testing. A major feature of these chapters is the division into methods of finding appropriate statistical techniques and methods of evaluating these techniques. Finding and evaluating are of interest to both the theorist and the practitioner, but we feel that it is important to separate these endeavors. Different concerns are important, and different rules are invoked. Of further interest may be the sections of these chapters titled Other Considerations. Here, we indicate how the rules of statistical inference may be relaxed(as is done every day)and still produce meaningful inferences. Many of the techniques covered in these sections are ones that are used in consulting and are helpful in analyzing and inferring from actual problems The final three chapters can be thought of as special topics, although we feel that some familiarity with the material is important in anyone's statistical education Chapter 10 is a thorough introduction to decision theory and contains the most modern material we could include. Chapter 11 deals with the analysis of variance(oneway and randomized block), building the theory of the complete analysis from the more simple theory of treatment contrasts. Our experience has been that experimenters are most interested in inferences from contrasts, and using principles developed earlier most tests and intervals can be derived from contrasts. Finally, Chapter 12 treats the theory of regression, dealing first with simple linear regression and then covering regression with"errors in variables. This latter topic is quite important, not only to show its own usefulness and inherent difficulties. but also to illustrate the limitations of Inferences lrom ordinary regression As more concrete guidelines for basing a one-year course on this book, we offer the following suggestions. There can be two distinct types of courses taught from this book. One kind we might label"more mathematical, being a course appropriate for students majoring in statistics and having a solid mathematics background(at least 12 years of calculus, some matrix algebra, and perhaps a real analysis course). For such students we recommend covering Chapters 1-9 in their entirety (which should take approximately 22 weeks)and spend the remaining time customizing the course with selected topics from Chapters 10-12. Once the first nine chapters are covered the material in each of the last three chapters is self-contained, and can be covered in any order Another type of course is "more practical Such a course may also be a first course for mathematically sophisticated students, but is aimed at students with one year of calculus who may not be majoring in statistics. It stresses the more practical uses of statistical theory being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations. Such a course will necessaril omit a certain amount of material, but the following list of sections can be covered n a one-year course Chapter Sections All 2.1.2.2.2.3 3.1,3.2 4.1,4.2,43,4.5 5.1,5.2,5.3.1,54 61.1,621 7.1,7.2.1,7.2,2,7,2.3,7.3.1,7.3.3,7.4 81,821,8.2,3,8.24,83.1,83.2,84 9.1,921,9.2.2,9.24,9.3.1,94 11 11.1,11,2 2 121,12.2 If time permits, there can be some discussion(with little emphasis on details) of the material in Sections 4. 4. 5.5. and 6.1.2.6.1.3. 6.1.4. The material in Sections 11.3 and 12. 3 may also be considered The exercises have been gathered from many sources and are quite plentit feel that, perhaps, the only way to master this material is through practice, and thus we have included much opportunity to do so. The exercises are as varied as we could make them, and many of them illustrate points that are either new or complementary to the. material in the text. Some exercises are even taken from research papers. (It makes you feel old when you can include exercises based on papers that were new research during your own student days! )Although the exercises are not subdivided like the chapters, their ordering oughly follows that of the chapter.(Subdi often give too many hints. )Furthermore, the exercises become(again, roughly)more challenging as their numbers become higher. As this is an introductory book with a relatively broad scope, the topics are not covered in great depth. However, we felt some obligation to guide the reader one step further in the topics that may be of interest. Thus, we have included many references, pointing to the path to deeper understanding of any particular topic.(The Encyclopedia of statistical Sciences, edited by Kotz, Johnson, and Read, provides a fine introduction to many topicS. To write this book, we have drawn on both our past teachings and current work. We have also drawn on many people, to whom we are extremely grateful. we thank our colleagues at Cornell, North Carolina State, and Purdue--in particular, Jim Berger, Larry Brown, Sir David Cox, Ziding Feng, Janet Johnson, Leon Gleser, Costas Goutis, Dave Lansky, George McCabe, Chuck McCulloch, Myra Samuels, Steve Schwager, and Shayle Searle, who have given their time and expertise in reading parts of this manuscript, offered assistance, and taken part in many conversations leading to constructive suggestions. We also thank Shanti Gupta for his hospitality and the library at Purdue, which was essential. We are grateful for the detailed reading and helpful suggestions of Shayle Searle and of our reviewers, both anonymous and non-anonymous (im Albert, Dan Coster, and Tom Wehrly ). We also thank David Moore and George McCabe for allowing us to use their tables, and Steve hirdt for supplying us with data. Since this book was written by two people who, for most of the time, were at least 600 miles apart, we lastly thank Bitnet for making this entire thing possible George Caselle Roger L. Berg ' I can see nothing " said l, handing it back to my friend On the contrary, Watson, you can see everything. You fail, however, to reason from what you see. You are too timid in drawing your inferences Dr. Watson and sherlock Holmes The adventure of the blue carbuncle 【实例截图】
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