Robust Statistical Methods with R
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Summary
Robust statistical methods were developed to supplement the classical procedures when the data violate classical assumptions. They are ideally suited to applied research across a broad spectrum of study, yet most books on the subject are narrowly focused, overly theoretical, or simply outdated. Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on practical application.
The authors work from underlying mathematical tools to implementation, paying special attention to the computational aspects. They cover the whole range of robust methods, including differentiable statistical functions, distance of measures, influence functions, and asymptotic distributions, in a rigorous yet approachable manner. Highlighting hands-on problem solving, many examples and computational algorithms using the R software supplement the discussion. The book examines the characteristics of robustness, estimators of real parameter, large sample properties, and goodness-of-fit tests. It also includes a brief overview of R in an appendix for those with little experience using the software.
Based on more than a decade of teaching and research experience, Robust Statistical Methods with R offers a thorough, detailed overview of robust procedures. It is an ideal introduction for those new to the field and a convenient reference for those who apply robust methods in their daily work.
Table of Contents
INTRODUCTION
MATHEMATICAL TOOLS OF ROBUSTNESS
Statistical Model
Illustration on Statistical Estimation
Statistical Functional
Fisher's Consistency
Some Distances of Probability Measures
Relations between Distances
Differentiable Statistical Functionals
Gâteau Derivative
Fréchet Derivative
Hadamard (Compact) Derivative
Large Sample Distribution of Empirical Functional
Computation and Software Notes
Problems and Complements
BASIC CHARACTERISTICS OF ROBUSTNESS
Influence Function
Discretized Form of Influence Function
Qualitative Robustness
Quantitative Characteristics of Robustness Based on Influence Function
Maximum Bias
Breakdown Point
Tail-Behavior Measure of a Statistical Estimator
Variance of Asymptotic Normal Distribution
Problems and Complements
ROBUST ESTIMATORS OF REAL PARAMETER
Introduction
M-Estimators
M-Estimator of Location Parameter
Finite Sample Minimax Property of M-Estimator
Moment Convergence of M-Estimators
Studentized M-Estimators
L-Estimators
Sequential M- and L-Estimators
R-Estimators
Numerical Illustration
Computation and Software Notes
Problems and Complements
ROBUST ESTIMATORS IN LINEAR MODEL
Introduction
Least Squares Method
M-Estimators
GM-Estimators
S-Estimators and MM-Estimators
L-Estimators, Regression Quantiles
Regression Rank Scores
Robust Scale Statistics
Estimators with High Breakdown Points
One-Step Versions of Estimators
Numerical Illustrations
Computation and Software Notes
Problems and Complements
MULTIVARIATE LOCATION MODEL
Introduction
Multivariate M-Estimators of Location and Scatter
High Breakdown Estimators of Multivariate Location and Scatter
Admissibility and Shrinkage
Numerical Illustrations and Software Notes
Problem and Complements
SOME LARGE SAMPLE PROPERTIES OF ROBUST PROCEDURES
Introduction
M-Estimators
L-Estimators
R-Estimators
Interrelationships of M-, L-, and R-Estimators
Minimaximally Robust Estimators
Problems and Complements
SOME GOODNESS-OF-FIT TESTS
Introduction
Tests of Normality of the Shapiro-Wilk Type with Nuisance Regression and Scale Parameters
Goodness-of-Fit Tests for General Distribution with Nuisance Regression and Scale
Numerical Illustration
Computation and Software Notes
APPENDIX A: R SYSTEM
Brief R Overview
REFERENCES
SUBJECT INDEX
AUTHOR INDEX
Editorial Reviews
"[It is] an excellent introduction to robust statistical methods, eminently suited for an upper division undergraduate course. It discusses the basic ideas of Huber, Hampel, Bickel and Hajek in an accessible and rigorous form. For a beautiful introduction to the theory of M, L, and R estimation, there is no need to look any further."
-Jan de Leeuw, University at California at Los Angeles, Journal of Statistical Software, Vol. 16, July 2006
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