Robust and nonparametric statistical methods have their foundation in fields ranging from agricultural science to astronomy, from biomedical sciences to the public health disciplines, and, more recently, in genomics, bioinformatics, and financial statistics. These disciplines are presently nourished by data mining and high-level computer-based algorithms, but to work actively with robust and nonparametric procedures, practitioners need to understand their background. Explaining the underpinnings of robust methods and recent theoretical developments, Methodology in Robust and Nonparametric Statistics provides a profound mathematically rigorous explanation of the methodology of robust and nonparametric statistical procedures. Thoroughly up-to-date, this book Presents multivariate robust and nonparametric estimation with special emphasis on affine-equivariant procedures, followed by hypotheses testing and confidence sets Keeps mathematical abstractions at bay while remaining largely theoretical Provides a pool of basic mathematical tools used throughout the book in derivations of main results The methodology presented, with due emphasis on asymptotics and interrelations, will pave the way for further developments on robust statistical procedures in more complex models. Using examples to illustrate the methods, the text highlights applications in the fields of biomedical science, bioinformatics, finance, and engineering. In addition, the authors provide exercises in the text.
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
