ROBUST STATISTICAL METHODS WITH R

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Ouvrage 9781584884545 : ROBUST STATISTICAL METHODS WITH R
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


Auteur : JURECKOVA
Editeur : CHAPMAN \& HALL
Nombre de pages : 208
Date de publication : 11 2005

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