Methodology in Robust and Nonparametric Statistics

ISBN: 9780367381066 出版年：2012 页码：401 Jureckova, Jana Sen, Pranab Picek, Jan CRC Press

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