Robust Statistics

The Second Edition includes four new chapters on the following topics: robust tests; small sample asymptotics; breakdown point; and Bayesian robustness. A new section on time series has also been included. The first edition of this book was the first systematic, book-length treatment of robust statistics. The book begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. A solid foundation of robust statistics for both the theoretical and the applied statistician is provided. The book successfully reorganizes, summarizes, and extends information that has been available in part thus far. Concepts are stressed throughout rather than mathematical completeness, and selected numerical algorithms for computing robust estimates, as well as convergence proofs, are provided. Quantitative robustness information for a variety of estimates is contained within tables throughout.

Peter J. Huber, PhD, has over thirty-five years of academic experience and has previously served as professor of statistics at ETH Zurich (Switzerland), Harvard University, Massachusetts Institute of Technology, and the University of Bayreuth (Germany). An established authority in the field of robust statistics, Dr. Huber is the author or coauthor of four books and more than seventy journal articles in the areas of statistics and data analysis. Elvezio M. Ronchetti, PhD, is Professor of Statistics in the Department of Econometrics at the University of Geneva in Switzerland. Dr. Ronchetti is a Fellow of the American Statistical Association and coauthor of Robust Statistics: The Approach Based on Influence Functions, also published by Wiley.

Preface
Preface to First Edition
Generalities
Why Robust Procedures?
What Should a Robust Procedure Achieve?
Qualitative Robustness
Quantitative Robustness
Infinitesimal Aspects
Optimal Robustness
Computation of Robust Estimates
Limitations to Robustness Theory
The Weak Topology and its Metrization
General Remarks
The Weak Topology
L_vy and Prohorov Metrics
The Bounded Lipschitz Metric
Fr_echet and GGteaux Derivatives
Hampel's Theorem
The Basic Types of Estimates
General Remarks
Maximum Likelihood Type Estimates (MEstimates)
Linear Combinations of Order Statistics (LEstimates)
Estimates Derived from Rank Tests (REstimates)
Asymptotically Efficient M, L, and REstimates
Asymptotic Minimax Theory for Estimating Location
General Remarks
Minimax Bias
Minimax Variance: Preliminaries
Distributions Minimizing Fisher Information
Determination of F0 by Variational Methods
Asymptotically Minimax MEstimates
On the Minimax Property for Land REstimates
Redescending MEstimates
Questions of Asymmetric Contamination
Scale Estimates
General Remarks
MEstimates of Scale
LEstimates of Scale
REstimates of Scale
Asymptotically Efficient Scale Estimates
Distributions Minimizing Fisher Information for Scale
Minimax Properties
Multiparameter Problems, in Particular Joint Estimation of Location and Scale
General Remarks
Consistency of MEstimates
Asymptotic Normality of MEstimates
Simultaneous MEstimates of Location and Scale
MEstimates with Preliminary Estimates of Scale
Quantitative Robustness of Joint Estimates of Location and Scale
The Computation of MEstimates of Scale
Studentizing
Regression
General Remarks
The Classical Linear Least Squares Case
Residuals and Outliers
Robustizing the Least Squares Approach
Asymptotics of Robust Regression Estimates
Conjectures and Empirical Results
Asymptotic Covariances and Their Estimation
Concomitant Scale Estimates
Computation of Regression MEstimates
The Fixed Carrier Case: what size hi?
Analysis of Variance
L1estimates and Median Polish
Other Approaches to Robust Regression
Robust Covariance and Correlation Matrices
General Remarks
Estimation of Matrix Elements Through Robust Variances
Estimation of Matrix Elements Through Robust Correlation
An Affinely Equivariant Approach
Estimates Determined by Implicit Equations
Existence and Uniqueness of Solutions
Influence Functions and Qualitative Robustness
Consistency and Asymptotic Normality
Breakdown Point
Least Informative Distributions
Some Notes on Computation
Robustness of Design
General Remarks
Minimax Global Fit
Minimax Slope
Exact Finite S
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Summary

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Table of Contents

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