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E-raamat: Methodology in Robust and Nonparametric Statistics

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  • Formaat: 410 pages
  • Ilmumisaeg: 20-Jul-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439840696
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Methodology in Robust and Nonparametric StatisticsSuurem pilt
  • Formaat: 410 pages
  • Ilmumisaeg: 20-Jul-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439840696
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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.

Arvustused

"... a useful addition to the present theoretical literature on robust methods ..." -David E. Booth, Technometrics, November 2014 "... 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

Preface xi
Preface to the First Edition xiii
Acknowledgments xv
1 Introduction and Synopsis
1(8)
1.1 Introduction
1(4)
1.2 Synopsis
5(4)
2 Preliminaries
9(60)
2.1 Introduction
9(1)
2.2 Inference in Linear Models
9(6)
2.3 Robustness Concepts
15(10)
2.3.1 Finite-Sample Breakdown and Tail-Performance
20(5)
2.4 Robust and Minimax Estimation of Location
25(4)
2.5 Clippings from Probability and Asymptotic Theory
29(38)
2.5.1 Modes of Convergence of Stochastic Elements
31(3)
2.5.2 Basic Probability Inequalities
34(2)
2.5.3 Some Useful Inequalities and Lemmas
36(4)
2.5.4 Laws of Large Numbers and Related Inequalities
40(2)
2.5.5 Central Limit Theorems
42(6)
2.5.6 Limit Theorems Allied to Central Limit Theorems
48(2)
2.5.7 Central Limit Theorems for Quadratic Forms
50(1)
2.5.8 Contiguity of Probability Measures
51(1)
2.5.9 Hajek--Inagaki--LeCam theorem and the LAN condition
52(1)
2.5.10 Weak Convergence of Probability Measures
53(4)
2.5.11 Some Important Gaussian Functions
57(2)
2.5.12 Weak Invariance Principles
59(1)
2.5.13 Empirical Distributional Processes
60(4)
2.5.14 Weak Invariance Principle: Random Change of Time
64(1)
2.5.15 Embedding Theorems and Strong Invariance Principles
64(2)
2.5.16 Asymptotic Relative Efficiency: Concept and Measures
66(1)
2.6 Problems
67(2)
3 Robust Estimation of Location and Regression
69(48)
3.1 Introduction
69(1)
3.2 M-Estimators
70(8)
3.3 L-Estimators
78(13)
3.4 R-Estimators
91(13)
3.5 Minimum Distance and Pitman Estimators
104(4)
3.5.1 Minimum Distance Estimation
104(2)
3.5.2 Pitman Estimators
106(1)
3.5.3 Pitman-Type Estimators of Location
106(1)
3.5.4 Bayes-Type Estimators of General Parameter
107(1)
3.6 Differentiable Statistical Functions
108(4)
3.7 Problems
112(5)
4 Asymptotic Representations for L-Estimators
117(44)
4.1 Introduction
117(2)
4.2 Bahadur Representations for Sample Quantiles
119(4)
4.3 L-Statistics with Smooth Scores
123(6)
4.4 General L-Estimators
129(1)
4.5 Statistical Functionals
130(5)
4.6 Second-Order Asymptotic Distributional Representations
135(7)
4.7 L-Estimation in Linear Model
142(10)
4.8 Breakdown Point of L- and M-Estimators
152(3)
4.9 Further Developments
155(2)
4.10 Problems
157(4)
5 Asymptotic Representations for M-Estimators
161(48)
5.1 Introduction
161(1)
5.2 M-Estimation of General Parameters
161(8)
5.3 M-Estimation of Location: Fixed Scale
169(13)
5.3.1 Possibly Discontinuous but Monotone ψ
173(2)
5.3.2 Possibly Discontinuous and Nonmonotone ψ
175(2)
5.3.3 Second-Order Distributional Representations
177(5)
5.4 Studentized M-Estimators of Location
182(9)
5.5 M-Estimation in Linear Model
191(8)
5.6 Studentizing Scale Statistics
199(3)
5.7 Hadamard Differentiability in Linear Models
202(3)
5.8 Further Developments
205(1)
5.9 Problems
206(3)
6 Asymptotic Representations for R-Estimators
209(28)
6.1 Introduction
209(1)
6.2 Asymptotic Representations for R-Estimators of Location
210(7)
6.3 Representations for R-Estimators in Linear Model
217(7)
6.4 Regression Rank Scores
224(3)
6.5 Inference Based on Regression Rank Scores
227(6)
6.5.1 RR-Tests
229(1)
6.5.2 RR-Estimators
230(1)
6.5.3 Studentizing Scale Statistics and Regression Rank Scores
231(2)
6.6 Bibliographical Notes
233(1)
6.7 Problems
234(3)
7 Asymptotic Interrelations of Estimators
237(30)
7.1 Introduction
237(2)
7.2 Estimators of location
239(10)
7.3 Estimation in linear model
249(3)
7.4 Approximation by One-Step Versions
252(12)
7.5 Further developments
264(1)
7.6 Problems
265(2)
8 Robust Estimation: Multivariate Perspectives
267(48)
8.1 Introduction
267(1)
8.2 The Notion of Multivariate Symmetry
268(3)
8.3 Multivariate Location Estimation
271(5)
8.4 Multivariate Regression Estimation
276(3)
8.4.1 Normal Multivariate Linear Model
277(1)
8.4.2 General Multivariate Linear Model
277(2)
8.5 Affine-Equivariant Robust Estimation
279(12)
8.5.1 Smooth Affine-Equivariant L-Estimation of θ
281(7)
8.5.2 Affine-Equivariant Regression Estimation
288(2)
8.5.3 Additional Remarks and Comments
290(1)
8.6 Efficiency and Minimum Risk Estimation
291(5)
8.7 Stein-Rule Estimators and Minimum Risk Efficiency
296(10)
8.7.1 Location Model
297(4)
8.7.2 Extension to the Linear Model
301(5)
8.8 Robust Estimation of Multivariate Scatter
306(2)
8.9 Some Complementary and Supplementary Notes
308(2)
8.10 Problems
310(5)
9 Robust Tests and Confidence Sets
315(36)
9.1 Introduction
315(1)
9.2 M-Tests and R-Tests
316(12)
9.2.1 M-Tests of Location
316(3)
9.2.2 M-Tests in Linear Model
319(3)
9.2.3 R-Tests
322(2)
9.2.4 Robustness of Tests
324(3)
9.2.5 Some Remarks on the Wald-Type Tests
327(1)
9.3 Minimax Tests
328(1)
9.4 Robust Confidence Sets
329(13)
9.4.1 Type I Confidence Intervals
330(7)
9.4.2 Type II Confidence Intervals
337(5)
9.5 Multiparameter Confidence Sets
342(4)
9.6 Affine-Equivariant Tests and Confidence Sets
346(3)
9.7 Problems
349(2)
Appendix
351(6)
Uniform Asymptotic Linearity
351(6)
References 357(28)
Subject index 385(5)
Author index 390
Jure?ková, Jana; Sen, Pranab; Picek, Jan
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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