Analytical and Bootstrap Bias Corrections
Maximum likelihood estimators are usually biased: In finite samples, their expected value differs from the true parameter value. This is a systematic error. It typically vanishes as the sample size increases, but it can be large in small samples. Differen
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Gauss M. Cordeiro Francisco Cribari-Neto
An Introduction to Bartlett Correction and Bias Reduction
SpringerBriefs in Statistics
For further volumes: http://www.springer.com/series/8921
Gauss M. Cordeiro Francisco Cribari-Neto •
An Introduction to Bartlett Correction and Bias Reduction
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Gauss M. Cordeiro Francisco Cribari-Neto Departamento de Estatística Universidade Federal de Pernambuco Recife, Pernambuco Brazil
ISSN 2191-544X ISSN 2191-5458 (electronic) ISBN 978-3-642-55254-0 ISBN 978-3-642-55255-7 (eBook) DOI 10.1007/978-3-642-55255-7 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014938215 Mathematics Subject Classification (2010): 62F03, 62F10 The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This book is dedicated to Maurice S. Bartlett
Preface
Statistical inference is oftentimes based on first-order asymptotic theory. In particular, it is a common practice to perform likelihood ratio, score and Wald tests using approximate critical values. Such critical values are obtained from the test statistic limiting distribution when the null hypothesis is true. The approximation holds when the number of observations in the sample tends to infinity, and it is thus expected to deliver reliable infe
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