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Methodology in Robust and Nonparametric Statistics

By Jana Jurečková, Pranab Kumar Sen, Jan Picek

CRC Press – 2012 – 410 pages

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    978-1-43-984068-9
    July 19th 2012

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.

Reviews

"… this book is very detailed and offers many ingenious ways to set up expansions for robust estimators leading to asymptotic properties of statistics. In view of the broadness of the study undertaken over a number of years, there is something for everyone. … To help the reader assimilate the ideas, there are ample problems at the end of each chapter."

—Brenton R. Clarke, Australian & New Zealand Journal of Statistics, 2014

"There were several ideas that are rarely presented in other texts, but that I found of special interest. Many of these appear in the extended material on rank tests and functionals, and I found the development of rank tests from the regression quantile dual to be especially fruitful and elegant. … I have always found that mathematical results are the hardest part of statistics to learn (or to teach), and that the best way to do this is through a clear and very systematic development with a careful balance between breadth and conceptual simplicity. This text provides just such an approach for the area of robust statistics."

—Stephen Portnoy, Journal of the American Statistical Association, September 2013

"In summary, this book is mathematically rigorous with emphasis on the asymptotic theory of robust statistical inference. It is an excellent book for more mathematically oriented readers who intend to do further study in the field. For practitioners in the pharmaceutical industry, a solid theoretical background in mathematics and statistics is needed in order to gain a thorough understanding of the topics covered."

Journal of Biopharmaceutical Statistics

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 Kumar 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