『Robust Statistical Methods with R』

目

Jana Jureckova & Jan Picek

（2005年11月29日刊行，Chapman & Hall/CRC， ISBN:1584884541）


【目次】
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
G穰eau Derivative
Fr馗het 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