The second edition of Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on new developments and on the computational aspects. There are many numerical examples and notes on the R environment, and the updated chapter on the multivariate model contains additional material on visualization of multivariate data in R. A new chapter on robust procedures in measurement error models concentrates mainly on the rank procedures, less sensitive to errors than other procedures. This book will be an invaluable resource for researchers and postgraduate students in statistics and mathematics. Features:
• Provides a systematic, practical treatment of robust statistical methods
• Offers a rigorous treatment of the whole range of robust methods, including the sequential versions of estimators, their moment convergence, and compares their asymptotic and finite-sample behavior
• The extended account of multivariate models includes the admissibility, shrinkage effects and unbiasedness of two-sample tests
• Illustrates the small sensitivity of the rank procedures in the measurement error model
• Emphasizes the computational aspects, supplies many examples and illustrations, and provides the own procedures of the authors in the R software on the book's website.
Author(s): Jana Jurečková, Jan Picek, Martin Schindler
Edition: 2
Publisher: CRC Press/Taylor & Francis Group
Year: 2019
Language: English
Pages: xiv+254
Tags: Robust Statistics, Mathematical Statistics, R (Computer Program Language)
Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Preface to the 1st edition
Acknowledgments
Introduction
R environment
1. Mathematical tools of robustness
1.1 Statistical model
1.2 Illustration on statistical estimation
1.3 Statistical functional
1.4 Fisher consistency
1.5 Some distances of probability measures
1.6 Relations between distances
1.7 Differentiable statistical functionals
1.8 Gâteau derivative
1.9 Fréchet derivative
1.10 Hadamard (compact) derivative
1.11 Large sample distribution of empirical functional
1.12 Problems and complements
2. Characteristics of robustness
2.1 Influence function
2.2 Discretized form of influence function
2.3 Qualitative robustness
2.4 Quantitative characteristics of robustness based on influence function
2.5 Maximum bias
2.6 Breakdown point
2.7 Tail–behavior measure of a statistical estimator
2.8 Variance of asymptotic normal distribution
2.9 Available “robust” packages in R
2.10 Problems and complements
3. Estimation of real parameter
3.1 M-estimators
3.2 M-estimator of location
3.3 Finite sample minimax property of M-estimator
3.4 Moment convergence of M-estimators
3.5 Studentized M-estimators
3.6 S- and T- estimators, MM-estimators
3.7 L-estimators
3.8 Moment convergence of L-estimators
3.9 Sequential M- and L-estimators, minimizing observation costs
3.10 R-estimators
3.11 Examples
3.12 Problems and complements
4. Linear model
4.1 Introduction
4.2 Least squares method
4.3 M-estimators
4.4 GM-estimators
4.5 R-estimators, GR-estimators
4.6 L-estimators, regression quantiles
4.7 Regression rank scores
4.8 Robust scale statistics
4.9 Estimators with high breakdown points
4.10 S-estimators and MM-estimators
4.11 Examples
4.12 Problems and complements
5. Multivariate model
5.1 Concept of multivariate symmetry
5.2 Multivariate location estimation
5.3 Admissibility and shrinkage
5.4 Visualization of multivariate data in R
5.5 Multivariate regression estimation
5.6 Affine invariance and equivariance, maximal invariants
5.7 Unbiasedness of two-sample nonparametric tests
5.8 Problems and complements
6. Large sample and finite sample behavior of robust estimators
6.1 Introduction
6.2 M-estimators
6.3 L-estimators
6.4 R-estimators
6.5 Interrelationships of M-, L- and R-estimators
6.6 Estimation under contaminated distribution
6.7 Possible non-admissibility under finite-sample
6.8 Newton-Raphson iterations of estimating equations
6.9 Adaptive combination of estimation procedures
6.10 Numerical illustration of LAD and LS regression
6.11 Problems and complements
7. Robust and nonparametric procedures in measurement error models
7.1 Introduction
7.2 Types of measurement errors, misspecification and violation of assumptions
7.3 Measurement errors in nonparametric testing
7.4 Measurement errors in nonparametric estimation
7.5 Problems and complements
Appendix A: Authors’ own procedures in R
Bibliography
Author index
Subject index
