Methodology in Robust and Nonparametric Statistics

Introduction and Synopsis
Introduction
Synopsis

Preliminaries
Introduction
Inference in Linear Models
Robustness Concepts
Robust and Minimax Estimation of Location
Clippings from Probability and Asymptotic Theory
Problems

Robust Estimation of Location and Regression
Introduction
M-Estimators
L-Estimators
R-Estimators
Minimum Distance and Pitman Estimators
Differentiable Statistical Functions
Problems

Asymptotic Representations for L-Estimators
Introduction
Bahadur Representations for Sample Quantiles
L-Statistics with Smooth Scores
General L-Estimators
Statistical Functionals
Second-Order Asymptotic Distributional Representations
L-Estimation in Linear Model
Breakdown Point of L- and M-Estimators
Further Developments
Problems

Asymptotic Representations for M-Estimators
Introduction
M-Estimation of General Parameters
M-Estimation of Location: Fixed Scale
Studentized M-Estimators of Location
M-Estimation in Linear Model
Studentizing Scale Statistics
Hadamard Differentiability in Linear Models
Further Developments
Problems

Asymptotic Representations for R-Estimators
Introduction
Asymptotic Representations for R-Estimators of Location
Representations for R-Estimators in Linear Model
Regression Rank Scores
Inference Based on Regression Rank Scores
Bibliographical Notes
Problems

Asymptotic Interrelations of Estimators
Introduction
Estimators of location
Estimation in linear model
Approximation by One-Step Versions
Further developments
Problems

Robust Estimation: Multivariate Perspectives
Introduction
The Notion of Multivariate Symmetry
Multivariate Location Estimation
Multivariate Regression Estimation
Affine-Equivariant Robust Estimation
Efficiency and Minimum Risk Estimation
Stein-Rule Estimators and Minimum Risk Efficiency
Robust Estimation of Multivariate Scatter
Some Complementary and Supplementary Notes
Problems

Robust Tests and Confidence Sets
Introduction
M-Tests and R-Tests
Minimax Tests
Robust Confidence Sets
Multiparameter Confidence Sets
Affine-Equivariant Tests and Confidence Sets
Problems

Robust Estimation: Multivariate Perspectives
Introduction
The Notion of Multivariate Symmetry
Multivariate Location Estimation
Multivariate Regression Estimation
Affine-Equivariant Robust Estimation
Efficiency and Minimum Risk Estimation
Stein-Rule Estimators and Minimum Risk Efficiency
Robust Estimation of Multivariate Scatter
Some Complementary and Supplementary Notes
Problems

Robust Tests and Confidence Sets
Introduction
M-Tests and R-Tests
Minimax Tests
Robust Confidence Sets
Multiparameter Confidence Sets
Affine-Equivariant Tests and Confidence Sets
Problems