实例介绍
【实例简介】
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|STCS Second edition Peter j, huber Professor of Statistics, retired Klosters Switzerland EⅣ ezio m. Ronchetti Professor of Statistics University of Geneva, Switzerland WILEY A JOHn WileY SONS INC. PUBliCAtION Copyrightc 2009 by John Wiley Sons, Inc. All rights reserved Published by John Wiley sons, Inc, Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax 978)750-4470,oronthewebatwww.copyrig om. requests to the publisher for permission should be addressed to the permissions department John Wiley sons, Inc., 11 1 River Street, Hoboken, NJ 07030,(201)748-6011,fax(201)748-6008,oronlineathttp:/www.wileycom/go/permission Limit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer 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 may not be available in electronic format. For information about wiley products, visit our web site at www.wileycom Library of Congress Cataloging-in-Publication Data: Huber Peter J Robust statistics, second edition/ Peter J. Huber, Elvezio ronchetti p. cn Includes bibliographical references and inde ISBN978-0-470-12990-6( cloth) 1. Robust statistics. I. Ronchetti. elvezio. II. Title QA276.H7852009 519.5-dc22 2008033283 Printed in the United States of america 10987654321 To the memory o1 John w. tukey This Page Intentionally Left Blank CONTENTS Preface Preface to first edition Generalities 1 Why robust Procedures 1. 2 What Should a robust procedure achieve? 1.2.1 Robust. Nonparametric and Distribution-Free 1.2.2 Adaptive procedures 1.2.3 Resistant Procedures 1.2. 4 Robustness versus Diagnostics 1.2.5 Breakdown point 1.3 Qualitative Robustness 56788891 1. 4 Quantitative Robustness 1.5 Infinitesimal Aspects 14 1.6 Optimal Robustness 17 1.7 Performance Comparisons 18 CONTENTS 1.8 Computation of robust estimates 18 1.9 Limitations to Robustness Theory 20 2 The Weak Topology and its Metrization 23 eneral remarks 23 2.2 The Weak Topology 23 2.3 Levy and prohorov metrics 27 2.4 The bounded Lipschitz metric 32 2.5 Frechet and Gateaux derivatives 36 6 Hampels Theorem 41 3 The Basic Types of Estimates 45 3. 1 General Remarks 45 3.2 Maximum Likelihood Type Estimates(M-Estimates) 3.2.1 Influence Function of m-estimates 7 3.2.2 Asymptotic Properties of M-Estimates 48 3.2.3 Quantitative and Qualitative Robustness of M Estimates 3.3 Linear Combinations of Order Statistics(L-Estimates) 3.3.1 Influence Function of -Estimates 3.3.2 Quantitative and Qualitative robustness of l-Estimates 59 3. 4 Estimates Derived from Rank Tests(R-estimates 3.4.1 Influence Function of R-Estimates 62 3.4.2 Quantitative and Qualitative robustness of R-Estimates 64 3.5 Asymptotically Efficient M-, L,and R-Estimates 67 4 Asymptotic Minimax Theory for Estimating Location 4.1 General remarks 4.2 Minimax bias 4.3 Minimax Variance: Preliminaries 74 4. 4 Distributions minimizing fisher Information 76 4.5 Determination of Fo by Variational Methods 81 4.6 Asymptotically Minimax M-Estimates 91 4.7 On the minimax Property for L-and R-estimates 95 4.8 Redescending m-estimates 7 4.9 Questions of Asymmetric Contamination 101 CONTENTS Scale Estimates 105 5.1 General remarks 105 5.2 M-Estimates of scale 107 5.3 L-Estimates of scale 5.4 R-Estimates of Scale 112 5.5 Asymptotically efficient Scale estimates 114 5.6 Distributions Minimizing fisher Information for Scale 5.7 Minimax Properties 11 6 Multiparameter Problemsin Particular Joint Estimation of Location and scale 125 6. 1 General remarks 125 6.2 Consistency of M-Estimates 126 6.3 Asymptotic Normality of M-Estimates 130 6. 4 Simultaneous m-Estimates of Location and scale 133 6.5 M-Estimates with Preliminary Estimates of Scale 137 6.6 Quantitative robustness of Joint Estimates of Location and Scale 139 6.7 The Computation of M-Estimates of Scale 143 68 Studentizing 145 7 Regression 149 7. 1 General remarks 149 7. 2 The Classical Linear Least Squares Case 154 7. 2.1 Residuals and Outliers 158 7.3 Robustizing the Least Squares Approach 160 7.4 Asymptotics of robust regression Estimates 163 741 The Cases hp2→0 and hp→0 7.5 Conjectures and Empirical Results 168 7.5.1 Symmetric Error Distributions 168 7.5.2 The Question of Bias 168 7.6 Asymptotic Covariances and Their estimation 170 7. 7 Concomitant Scale estimates 172 7.8 Computation of Regression M-Estimates 175 7.8.1 The Scale Step 176 7.8.2 The Location Step with Modified residuals 178 7.8.3 The Location Step with Modified Weights 179 CONTENTS 7.9 The Fixed Carrier Case: What Size hi? 186 7. 10 Analysis of Variance 190 7. 11 LI-estimates and Median polish 193 7. 12 Other Approaches to Robust Regression 195 8 Robust Covariance and Correlation Matrices 199 8. 1 General remarks 8.2 Estimation of Matrix Elements Through robust Variances 203 8.3 Estimation of Matrix Elements Through robust Correlation 204 8.4 An Affinely equivariant approach 210 8.5 Estimates Determined by Implicit Equations 212 8.6 Existence and Uniqueness of Solutions 214 8.6. 1 The Scatter estimate v 214 8.6.2 The Location estimate t 219 8.6.3 Joint Estimation of t and y 220 8.7 Influence Functions and Qualitative robustness 220 8.8 Consistency and asymptotic normality 223 8.9 Breakdown Point 4 8.10 Least informative distributions 225 8.10 5 8. 10.2 Covariance 227 8.11 Some Notes on Computation 233 9 Robustness of Design 239 9.1 General remarks 239 9.2 Minimax Global Fit 9.3 Minimax Slope 246 10 Exact Finite Sample Results 249 10.1 General Remarks 249 10.2 Lower and Upper Probabilities and Capacities 250 10.2.1 2-Monotone and 2-Alternating Capacities 255 10.2.2 Monotone and Alternating Capacities of Infinite Order 258 10.3 Robust Tests 259 10.3. 1 Particular Cases 265 10.4 Sequential Tests 267 【实例截图】
【核心代码】
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|STCS Second edition Peter j, huber Professor of Statistics, retired Klosters Switzerland EⅣ ezio m. Ronchetti Professor of Statistics University of Geneva, Switzerland WILEY A JOHn WileY SONS INC. PUBliCAtION Copyrightc 2009 by John Wiley Sons, Inc. All rights reserved Published by John Wiley sons, Inc, Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax 978)750-4470,oronthewebatwww.copyrig om. requests to the publisher for permission should be addressed to the permissions department John Wiley sons, Inc., 11 1 River Street, Hoboken, NJ 07030,(201)748-6011,fax(201)748-6008,oronlineathttp:/www.wileycom/go/permission Limit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer 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 may not be available in electronic format. For information about wiley products, visit our web site at www.wileycom Library of Congress Cataloging-in-Publication Data: Huber Peter J Robust statistics, second edition/ Peter J. Huber, Elvezio ronchetti p. cn Includes bibliographical references and inde ISBN978-0-470-12990-6( cloth) 1. Robust statistics. I. Ronchetti. elvezio. II. Title QA276.H7852009 519.5-dc22 2008033283 Printed in the United States of america 10987654321 To the memory o1 John w. tukey This Page Intentionally Left Blank CONTENTS Preface Preface to first edition Generalities 1 Why robust Procedures 1. 2 What Should a robust procedure achieve? 1.2.1 Robust. Nonparametric and Distribution-Free 1.2.2 Adaptive procedures 1.2.3 Resistant Procedures 1.2. 4 Robustness versus Diagnostics 1.2.5 Breakdown point 1.3 Qualitative Robustness 56788891 1. 4 Quantitative Robustness 1.5 Infinitesimal Aspects 14 1.6 Optimal Robustness 17 1.7 Performance Comparisons 18 CONTENTS 1.8 Computation of robust estimates 18 1.9 Limitations to Robustness Theory 20 2 The Weak Topology and its Metrization 23 eneral remarks 23 2.2 The Weak Topology 23 2.3 Levy and prohorov metrics 27 2.4 The bounded Lipschitz metric 32 2.5 Frechet and Gateaux derivatives 36 6 Hampels Theorem 41 3 The Basic Types of Estimates 45 3. 1 General Remarks 45 3.2 Maximum Likelihood Type Estimates(M-Estimates) 3.2.1 Influence Function of m-estimates 7 3.2.2 Asymptotic Properties of M-Estimates 48 3.2.3 Quantitative and Qualitative Robustness of M Estimates 3.3 Linear Combinations of Order Statistics(L-Estimates) 3.3.1 Influence Function of -Estimates 3.3.2 Quantitative and Qualitative robustness of l-Estimates 59 3. 4 Estimates Derived from Rank Tests(R-estimates 3.4.1 Influence Function of R-Estimates 62 3.4.2 Quantitative and Qualitative robustness of R-Estimates 64 3.5 Asymptotically Efficient M-, L,and R-Estimates 67 4 Asymptotic Minimax Theory for Estimating Location 4.1 General remarks 4.2 Minimax bias 4.3 Minimax Variance: Preliminaries 74 4. 4 Distributions minimizing fisher Information 76 4.5 Determination of Fo by Variational Methods 81 4.6 Asymptotically Minimax M-Estimates 91 4.7 On the minimax Property for L-and R-estimates 95 4.8 Redescending m-estimates 7 4.9 Questions of Asymmetric Contamination 101 CONTENTS Scale Estimates 105 5.1 General remarks 105 5.2 M-Estimates of scale 107 5.3 L-Estimates of scale 5.4 R-Estimates of Scale 112 5.5 Asymptotically efficient Scale estimates 114 5.6 Distributions Minimizing fisher Information for Scale 5.7 Minimax Properties 11 6 Multiparameter Problemsin Particular Joint Estimation of Location and scale 125 6. 1 General remarks 125 6.2 Consistency of M-Estimates 126 6.3 Asymptotic Normality of M-Estimates 130 6. 4 Simultaneous m-Estimates of Location and scale 133 6.5 M-Estimates with Preliminary Estimates of Scale 137 6.6 Quantitative robustness of Joint Estimates of Location and Scale 139 6.7 The Computation of M-Estimates of Scale 143 68 Studentizing 145 7 Regression 149 7. 1 General remarks 149 7. 2 The Classical Linear Least Squares Case 154 7. 2.1 Residuals and Outliers 158 7.3 Robustizing the Least Squares Approach 160 7.4 Asymptotics of robust regression Estimates 163 741 The Cases hp2→0 and hp→0 7.5 Conjectures and Empirical Results 168 7.5.1 Symmetric Error Distributions 168 7.5.2 The Question of Bias 168 7.6 Asymptotic Covariances and Their estimation 170 7. 7 Concomitant Scale estimates 172 7.8 Computation of Regression M-Estimates 175 7.8.1 The Scale Step 176 7.8.2 The Location Step with Modified residuals 178 7.8.3 The Location Step with Modified Weights 179 CONTENTS 7.9 The Fixed Carrier Case: What Size hi? 186 7. 10 Analysis of Variance 190 7. 11 LI-estimates and Median polish 193 7. 12 Other Approaches to Robust Regression 195 8 Robust Covariance and Correlation Matrices 199 8. 1 General remarks 8.2 Estimation of Matrix Elements Through robust Variances 203 8.3 Estimation of Matrix Elements Through robust Correlation 204 8.4 An Affinely equivariant approach 210 8.5 Estimates Determined by Implicit Equations 212 8.6 Existence and Uniqueness of Solutions 214 8.6. 1 The Scatter estimate v 214 8.6.2 The Location estimate t 219 8.6.3 Joint Estimation of t and y 220 8.7 Influence Functions and Qualitative robustness 220 8.8 Consistency and asymptotic normality 223 8.9 Breakdown Point 4 8.10 Least informative distributions 225 8.10 5 8. 10.2 Covariance 227 8.11 Some Notes on Computation 233 9 Robustness of Design 239 9.1 General remarks 239 9.2 Minimax Global Fit 9.3 Minimax Slope 246 10 Exact Finite Sample Results 249 10.1 General Remarks 249 10.2 Lower and Upper Probabilities and Capacities 250 10.2.1 2-Monotone and 2-Alternating Capacities 255 10.2.2 Monotone and Alternating Capacities of Infinite Order 258 10.3 Robust Tests 259 10.3. 1 Particular Cases 265 10.4 Sequential Tests 267 【实例截图】
【核心代码】
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