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Robust Statistical Methods with R (Hardcover)
by Jana Jureckova (Author), Jan Picek (Author)
Product Details
* Hardcover: 216 pages
* Publisher: Chapman & Hall/CRC; 1 edition (November 29, 2005)
* Language: English
* ISBN-10: 1584884541
* ISBN-13: 978-1584884545
Editorial Reviews
Review
[It is] an excellent introduction to robust statistical methods, eminently suited for an upper division undergraduate course. It discusses the basic ideas of Huber, Hampel, Bickel and Hajek in an accessible and rigorous form. For a beautiful introduction to the theory of M, L, and R estimation, there is no need to look any further.
-Jan de Leeuw, University at California at Los Angeles, Journal of Statistical Software, Vol. 16, July 2006
Product Description
Robust statistical methods were developed to supplement the classical procedures when the data violate classical assumptions. They are ideally suited to applied research across a broad spectrum of study, yet most books on the subject are narrowly focused, overly theoretical, or simply outdated. Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on practical application.
The authors work from underlying mathematical tools to implementation, paying special attention to the computational aspects. They cover the whole range of robust methods, including differentiable statistical functions, distance of measures, influence functions, and asymptotic distributions, in a rigorous yet approachable manner. Highlighting hands-on problem solving, many examples and computational algorithms using the R software supplement the discussion. The book examines the characteristics of robustness, estimators of real parameter, large sample properties, and goodness-of-fit tests. It also includes a brief overview of R in an appendix for those with little experience using the software.
Based on more than a decade of teaching and research experience, Robust Statistical Methods with R offers a thorough, detailed overview of robust procedures. It is an ideal introduction for those new to the field and a convenient reference for those who apply robust methods in their daily work.
Editorial Reviews
Review
[It is] an excellent introduction to robust statistical methods, eminently suited for an upper division undergraduate course. It discusses the basic ideas of Huber, Hampel, Bickel and Hajek in an accessible and rigorous form. For a beautiful introduction to the theory of M, L, and R estimation, there is no need to look any further.
-Jan de Leeuw, University at California at Los Angeles, Journal of Statistical Software, Vol. 16, July 2006
Contents
Preface
Authors
Introduction
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 Gˆateau derivative
1.9 Fr´echet derivative
1.10 Hadamard (compact) derivative
1.11 Large sample distribution of empirical functional
1.12 Computation and software notes
1.13 Problems and complements
2 Basic 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 Problems and complements
3 Robust estimators of real parameter
3.1 Introduction
3.2 M-estimators
3.3 M-estimator of location parameter
3.4 Finite sample minimax property of M-estimator
3.5 Moment convergence of M-estimators
3.6 Studentized M-estimators
3.7 L-estimators
3.8 Moment convergence of L-estimators
3.9 Sequential M- and L-estimators
3.10 R-estimators
3.11 Numerical illustration
3.12 Computation and software notes
3.13 Problems and complements
4 Robust estimators in linear model
4.1 Introduction
4.2 Least squares method
4.3 M-estimators
4.4 GM-estimators
4.5 S-estimators and MM-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 One-step versions of estimators
4.11 Numerical illustrations
4.12 Computation and software notes
4.13 Problems and complements
5 Multivariate location model
5.1 Introduction
5.2 Multivariate M-estimators of location and scatter
5.3 High breakdown estimators of multivariate location and scatter
5.4 Admissibility and shrinkage
5.5 Numerical illustrations and software notes
5.6 Problems and complements
6 Some large sample properties of robust procedures
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 Minimaximally robust estimators
6.7 Problems and complements
7 Some goodness-of-fit tests
7.1 Introduction
7.2 Tests of normality of the Shapiro-Wilk type with nuisance
regression and scale parameters
7.3 Goodness-of-fit tests for general distribution with nuisance
regression and scale
7.4 Numerical illustration
7.5 Computation and software notes
Appendix A: R system
A.1 Brief R overview
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