Methodology in Robust and Nonparametric Statistics
By Jana Jurečková, Pranab Sen, Jan Picek
Published July 20th 2012 by CRC Press – 410 pages
Description
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.
Contents
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
Name: Methodology in Robust and Nonparametric Statistics (Hardback) – CRC Press
Description: By Jana Jurečková, Pranab Sen, Jan Picek. 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...
Categories: Statistical Theory & Methods, Probability, Mathematics & Statistics for Engineers
