A new edition of the classic, groundbreaking book on robust
statistics
Over twenty-five years after the publication of its predecessor,
Robust Statistics, Second Edition continues to provide an
authoritative and systematic treatment of the topic. This new
edition has been thoroughly updated and expanded to reflect the
latest advances in the field while also outlining the established
theory and applications for building a solid foundation in robust
statistics for both the theoretical and the applied
statistician.
A comprehensive introduction and discussion on the formal
mathematical background behind qualitative and quantitative
robustness is provided, and subsequent chapters delve into basic
types of scale estimates, asymptotic minimax theory, regression,
robust covariance, and robust design. In addition to an extended
treatment of robust regression, the Second Edition features four
new chapters covering:
* Robust Tests
* Small Sample Asymptotics
* Breakdown Point
* Bayesian Robustness
An expanded treatment of robust regression and pseudo-values is
also featured, and concepts, rather than mathematical completeness,
are stressed in every discussion. Selected numerical algorithms for
computing robust estimates and convergence proofs are provided
throughout the book, along with quantitative robustness information
for a variety of estimates. A General Remarks section appears at
the beginning of each chapter and provides readers with ample
motivation for working with the presented methods and
techniques.
Robust Statistics, Second Edition is an ideal book for
graduate-level courses on the topic. It also serves as a valuable
reference for researchers and practitioners who wish to study the
statistical research associated with robust statistics.
Autorentext
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.
Zusammenfassung
A new edition of the classic, groundbreaking book on robust statistics
Over twenty-five years after the publication of its predecessor, Robust Statistics, Second Edition continues to provide an authoritative and systematic treatment of the topic. This new edition has been thoroughly updated and expanded to reflect the latest advances in the field while also outlining the established theory and applications for building a solid foundation in robust statistics for both the theoretical and the applied statistician.
A comprehensive introduction and discussion on the formal mathematical background behind qualitative and quantitative robustness is provided, and subsequent chapters delve into basic types of scale estimates, asymptotic minimax theory, regression, robust covariance, and robust design. In addition to an extended treatment of robust regression, the Second Edition features four new chapters covering:
-
Robust Tests
-
Small Sample Asymptotics
-
Breakdown Point
-
Bayesian Robustness
An expanded treatment of robust regression and pseudo-values is also featured, and concepts, rather than mathematical completeness, are stressed in every discussion. Selected numerical algorithms for computing robust estimates and convergence proofs are provided throughout the book, along with quantitative robustness information for a variety of estimates. A General Remarks section appears at the beginning of each chapter and provides readers with ample motivation for working with the presented methods and techniques.
Robust Statistics, Second Edition is an ideal book for graduate-level courses on the topic. It also serves as a valuable reference for researchers and practitioners who wish to study the statistical research associated with robust statistics.
Inhalt
Preface.
Preface to First Edition.
1. Generalities.
1.1 Why Robust Procedures?
1.2 What Should a Robust Procedure Achieve?
1.3 Qualitative Robustness.
1.4 Quantitative Robustness.
1.5 Infinitesimal Aspects.
1.6 Optimal Robustness.
1.7 Computation of Robust Estimates.
1.8 Limitations to Robustness Theory.
2. The Weak Topology and its Metrization.
2.1 General Remarks.
2.2 The Weak Topology.
2.3 Lévy and Prohorov Metrics.
2.4 The Bounded Lipschitz Metric.
2.5 Fréechet and Gâteaux Derivatives.
2.6 Hampel's Theorem.
3. The Basic Types of Estimates.
3.1 General Remarks.
3.2 Maximum Likelihood Type Estimates (MEstimates).
3.3 Linear Combinations of Order Statistics (LEstimates).
3.4 Estimates Derived from Rank Tests (REstimates).
3.5 Asymptotically Efficient M, L, and REstimates.
4. Asymptotic Minimax Theory for Estimating Location.
4.1 General Remarks.
4.2 Minimax Bias.
4.3 Minimax Variance: Preliminaries.
4.4 Distributions Minimizing Fisher Information.
4.5 Determination of F0 by Variational Methods.
4.6 Asymptotically Minimax MEstimates.
4.7 On the Minimax Property for Land REstimates.
4.8 Redescending MEstimates.
4.9 Questions of Asymmetric Contamination.
5. Scale Estimates.
5.1 General Remarks.
5.2 MEstimates of Scale.
5.3 LEstimates of Scale.
5.4 REstimates of Scale.
5.5 Asymptotically Efficient Scale Estimates.
5.6 Distributions Minimizing Fisher Information for Scale.
5.7 Minimax Properties.
6. Multiparameter Problems, in Particular Joint Estimation of Location and Scale.
6.1 General Remarks.
6.2 Consistency of MEstimates.
6.3 Asymptotic Normality of MEstimates.
6.4 Simultaneous MEstimates of Location and Scale.
6.5 MEstimates with Preliminary Estimates of Scale.
6.6 Quantitative Robustness of Joint Estimates of Location and Scale.
6.7 The Computation of MEstimates of Scale.
6.8 Studentizing.
7. Regression.
7.1 General Remarks.
7.2 The Classical Linear Least Squares Case.
7.2.1 Residuals and Outliers.
7.3 Robustizing the Least Squares Approach.
7.4 Asymptotics of Robust Regression Estimates.
7.5 Conjectures and Empirical Results.
7.6 Asymptotic Covariances and Their Estimation.
7.7 Concomitant Scale Estimates.
7.8 Computation of Regression MEstimates.
7.9 The Fixed Carrier Case: what size hi?
7.10 Analysis of Variance.
7.11 L1estimates and Median Polish.
7.12 Other Approaches to Robust Regression.
8. Robust Covariance and Correlation Matrices.
8.1 General Remarks.
8.2 Estimation of Matrix Elements Through Robust Variances.
8.3 Estimation of Matrix Elements Through Robust Correlation.
8.4 An Affinely Equivariant Approach.
8.5 Estimates Determined by Implicit Equations.
8.6 Existence and Uniqueness of Solutions.
8.7 Influence Functions and Qualitative Robustness.
8.8 Consistency and Asympt…