Theoretical Statistics Topics for a Core Course
Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis an
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Robert W. Keener
Theoretical Statistics Topics for a Core Course
Robert W. Keener Department of Statistics University of Michigan Ann Arbor, MI 48109-1092 USA Series Editors: George Casella Department of Statistics University of Florida Gainesville, FL 32611-8545 USA
Stephen Fienberg Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890 USA
Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305 USA
ISSN 1431-875X ISBN 978-0-387-93838-7 e-ISBN 978-0-387-93839-4 DOI 10.1007/978-0-387-93839-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010935925 © Springer Science+Business Media, LLC 2010 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, LLC, 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 adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed 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 on acid-free paper
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To Michael, Herman, Carl, and Billy
Preface
This book evolved from my notes for a three-semester sequence of core courses on theoretical statistics for doctoral students at the University of Michigan. When I first started teaching these courses, I used Theory of Point Estimation and Testing Statistical Hypotheses by Lehmann as texts, classic books that have certainly influenced my writings. To appreciate this book students will need a background in advanced calculus, linear algebra, probability, and some analysis. Some of this material is reviewed in the appendices. And, although the content on statistics is reasonably self-contained, prior knowledge of theoretical and applied statistics will be essential for most readers. In teaching core courses, my philosophy has been to try to expose students to as many of the central theoretical ideas and topics in the discipline as possible. Given the growth of statistics in recent years, such exposition can only be achieved in three semesters by sacrificing depth. Although basic material presented in early chapters of the book is covered carefully, many of the later chapters provide brief introductions to areas that could take a full semester to develop in detail. The role of measure theory in advanced statistics courses deserves careful consideration. Although few students will need great expertise in probability and measure, all should graduate conversant enough with the basics to read and understand researc
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