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E-book: Robust Statistical Methods with R, Second Edition

(Charles University, Prague, Czech Republic), , (Technical University, Liberec, Czech Republic)
  • Format: 268 pages
  • Pub. Date: 29-May-2019
  • Publisher: CRC Press
  • Language: eng
  • ISBN-13: 9781351975124
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Robust Statistical Methods with R, Second EditionLarger Image
  • Format: 268 pages
  • Pub. Date: 29-May-2019
  • Publisher: CRC Press
  • Language: eng
  • ISBN-13: 9781351975124
Other books in subject:

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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

Preface ix
Preface to the 1st edition xi
Acknowledgments xiii
Introduction 1(4)
R environment
3(2)
1 Mathematical tools of robustness
5(20)
1.1 Statistical model
5(5)
1.2 Illustration on statistical estimation
10(1)
1.3 Statistical functional
11(1)
1.4 Fisher consistency
12(1)
1.5 Some distances of probability measures
13(2)
1.6 Relations between distances
15(1)
1.7 Differentiable statistical functionals
16(1)
1.8 Gateau derivative
17(2)
1.9 Frechet derivative
19(1)
1.10 Hadamard (compact) derivative
20(1)
1.11 Large sample distribution of empirical functional
20(2)
1.12 Problems and complements
22(3)
2 Characteristics of robustness
25(18)
2.1 Influence function
25(1)
2.2 Discretized form of influence function
26(2)
2.3 Qualitative robustness
28(2)
2.4 Quantitative characteristics of robustness based on influence function
30(1)
2.5 Maximum bias
31(2)
2.6 Breakdown point
33(1)
2.7 Tail-behavior measure of a statistical estimator
34(5)
2.8 Variance of asymptotic normal distribution
39(1)
2.9 Available "robust" packages in R
39(1)
2.10 Problems and complements
40(3)
3 Estimation of real parameter
43(50)
3.1 M-estimators
43(2)
3.2 M-estimator of location
45(8)
3.3 Finite sample minimax property of M-estimator
53(5)
3.4 Moment convergence of M-estimators
58(3)
3.5 Studentized M-estimators
61(7)
3.6 S- and τ-estimators, MM-estimators
68(3)
3.7 L-estimators
71(8)
3.8 Moment convergence of L-estimators
79(2)
3.9 Sequential M- and L-estimators, minimizing observation costs
81(2)
3.10 R-estimators
83(3)
3.11 Examples
86(4)
3.12 Problems and complements
90(3)
4 Linear model
93(52)
4.1 Introduction
93(2)
4.2 Least squares method
95(11)
4.3 M-estimators
106(9)
4.4 GM-estimators
115(3)
4.5 R-estimators, GR-estimators
118(3)
4.6 L-estimators, regression quantiles
121(4)
4.7 Regression rank scores
125(3)
4.8 Robust scale statistics
128(3)
4.9 Estimators with high breakdown points
131(3)
4.10 S-estimators and MM-estimators
134(3)
4.11 Examples
137(5)
4.12 Problems and complements
142(3)
5 Multivariate model
145(28)
5.1 Concept of multivariate symmetry
145(1)
5.2 Multivariate location estimation
146(1)
5.3 Admissibility and shrinkage
147(5)
5.4 Visualization of multivariate data in R
152(4)
5.5 Multivariate regression estimation
156(1)
5.6 Affine invariance and equivariance, maximal invariants
157(4)
5.7 Unbiasedness of two-sample nonparametric tests
161(9)
5.8 Problems and complements
170(3)
6 Large sample and finite sample behavior of robust estimators
173(28)
6.1 Introduction
173(2)
6.2 M-estimators
175(2)
6.3 L-estimators
177(2)
6.4 R-estimators
179(1)
6.5 Interrelationships of M-, L- and R-estimators
179(4)
6.6 Estimation under contaminated distribution
183(3)
6.7 Possible non-admissibility under finite-sample
186(2)
6.8 Newton-Raphson iterations of estimating equations
188(3)
6.9 Adaptive combination of estimation procedures
191(5)
6.10 Numerical illustration of LAD and LS regression
196(2)
6.11 Problems and complements
198(3)
7 Robust and nonparametric procedures in measurement error models
201(18)
7.1 Introduction
201(1)
7.2 Types of measurement errors, misspecification and violation of assumptions
202(2)
7.3 Measurement errors in nonparametric testing
204(7)
7.4 Measurement errors in nonparametric estimation
211(5)
7.5 Problems and complements
216(3)
Appendix A Authors' own procedures in R 219(8)
Bibliography 227(20)
Author index 247(4)
Subject index 251
Jana Jureková is a Professor of Statistics at the Charles University, Prague.
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