Robust Statistics - 2nd Edition

鲁棒统计，现代统计方法， Robust Statistics第二版，学习现代统计方法R○ BUST STAT|STCSSecond editionPeter j, huberProfessor of Statistics, retiredKlosters SwitzerlandEⅣ ezio m. RonchettiProfessor of StatisticsUniversity of Geneva, SwitzerlandWILEYA JOHn WileY SONS INC. PUBliCAtIONCopyrightc 2009 by John Wiley Sons, Inc. All rights reservedPublished by John Wiley sons, Inc, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the priorwritten permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax978)750-4470,oronthewebatwww.copyrigom. requests to the publisher for permission shouldbe addressed to the permissions department John Wiley sons, Inc., 11 1 River Street, Hoboken, NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp:/www.wileycom/go/permissionLimit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies contained herein may not be suitablefor your situation. You should consult with a professional where appropriate. Neither the publisher norauthor shall be liable for any loss of profit or any other commercial damages, including but not limitedto special, incidental, consequential, or other damagesFor general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For information about wiley products, visit our web site atwww.wileycomLibrary of Congress Cataloging-in-Publication Data:Huber Peter JRobust statistics, second edition/ Peter J. Huber, Elvezio ronchettip. cnIncludes bibliographical references and indeISBN978-0-470-12990-6( cloth)1. Robust statistics. I. Ronchetti. elvezio. II. TitleQA276.H7852009519.5-dc222008033283Printed in the United States of america10987654321To the memory o1John w. tukeyThis Page Intentionally Left BlankCONTENTSPrefacePreface to first editionGeneralities1 Why robust Procedures1. 2 What Should a robust procedure achieve?1.2.1 Robust. Nonparametric and Distribution-Free1.2.2 Adaptive procedures1.2.3 Resistant Procedures1.2. 4 Robustness versus Diagnostics1.2.5 Breakdown point1.3 Qualitative Robustness567888911. 4 Quantitative Robustness1.5 Infinitesimal Aspects141.6 Optimal Robustness171.7 Performance Comparisons18CONTENTS1.8 Computation of robust estimates181.9 Limitations to Robustness Theory202 The Weak Topology and its Metrization23eneral remarks232.2 The Weak Topology232.3 Levy and prohorov metrics272.4 The bounded Lipschitz metric322.5 Frechet and Gateaux derivatives366 Hampels Theorem413 The Basic Types of Estimates453. 1 General Remarks453.2 Maximum Likelihood Type Estimates(M-Estimates)3.2.1 Influence Function of m-estimates73.2.2 Asymptotic Properties of M-Estimates483.2.3 Quantitative and Qualitative Robustness of MEstimates3.3 Linear Combinations of Order Statistics(L-Estimates)3.3.1 Influence Function of -Estimates3.3.2 Quantitative and Qualitative robustness of l-Estimates 593. 4 Estimates Derived from Rank Tests(R-estimates3.4.1 Influence Function of R-Estimates623.4.2 Quantitative and Qualitative robustness of R-Estimates 643.5 Asymptotically Efficient M-, L,and R-Estimates674 Asymptotic Minimax Theory for Estimating Location4.1 General remarks4.2 Minimax bias4.3 Minimax Variance: Preliminaries744. 4 Distributions minimizing fisher Information764.5 Determination of Fo by Variational Methods814.6 Asymptotically Minimax M-Estimates914.7 On the minimax Property for L-and R-estimates954.8 Redescending m-estimates74.9 Questions of Asymmetric Contamination101CONTENTSScale Estimates1055.1 General remarks1055.2 M-Estimates of scale1075.3 L-Estimates of scale5.4 R-Estimates of Scale1125.5 Asymptotically efficient Scale estimates1145.6 Distributions Minimizing fisher Information for Scale5.7 Minimax Properties116 Multiparameter Problemsin Particular Joint Estimationof Location and scale1256. 1 General remarks1256.2 Consistency of M-Estimates1266.3 Asymptotic Normality of M-Estimates1306. 4 Simultaneous m-Estimates of Location and scale1336.5 M-Estimates with Preliminary Estimates of Scale1376.6 Quantitative robustness of Joint Estimates of Location and Scale 1396.7 The Computation of M-Estimates of Scale14368Studentizing1457 Regression1497. 1 General remarks1497. 2 The Classical Linear Least Squares Case1547. 2.1 Residuals and Outliers1587.3 Robustizing the Least Squares Approach1607.4 Asymptotics of robust regression Estimates163741 The Cases hp2→0 and hp→07.5 Conjectures and Empirical Results1687.5.1 Symmetric Error Distributions1687.5.2 The Question of Bias1687.6 Asymptotic Covariances and Their estimation1707. 7 Concomitant Scale estimates1727.8 Computation of Regression M-Estimates1757.8.1 The Scale Step1767.8.2 The Location Step with Modified residuals1787.8.3 The Location Step with Modified Weights179CONTENTS7.9 The Fixed Carrier Case: What Size hi?1867. 10 Analysis of Variance1907. 11 LI-estimates and Median polish1937. 12 Other Approaches to Robust Regression1958 Robust Covariance and Correlation Matrices1998. 1 General remarks8.2 Estimation of Matrix Elements Through robust Variances2038.3 Estimation of Matrix Elements Through robust Correlation2048.4 An Affinely equivariant approach2108.5 Estimates Determined by Implicit Equations2128.6 Existence and Uniqueness of Solutions2148.6. 1 The Scatter estimate v2148.6.2 The Location estimate t2198.6.3 Joint Estimation of t and y2208.7 Influence Functions and Qualitative robustness2208.8 Consistency and asymptotic normality2238.9 Breakdown Point48.10 Least informative distributions2258.1058. 10.2 Covariance2278.11 Some Notes on Computation2339 Robustness of Design2399.1 General remarks2399.2 Minimax Global Fit9.3 Minimax Slope24610 Exact Finite Sample Results24910.1 General Remarks24910.2 Lower and Upper Probabilities and Capacities25010.2.1 2-Monotone and 2-Alternating Capacities25510.2.2 Monotone and Alternating Capacities of Infinite Order 25810.3 Robust Tests25910.3. 1 Particular Cases26510.4 Sequential Tests267