Introduction to robust and quasi-robust statistical methods / William J.J. Rey.
Series UniversitextEditor: Berlin ; New York : Springer-Verlag, 1983Descripción: ix, 236 p. : ill. ; 25 cmISBN: 0387128662 (U.S. : pbk.)Tema(s): Robust statisticsOtra clasificación: *CODIGO*Table of contents 1. Introduction and Summary [1] 1.1. History and main contributions [1] 1.2. Why robust estimations? [4] 1.3. Summary [9] PART A The Theoretical Background 2. Sample spaces, distributions, estimators [16] 2.1. Introduction [16] 2.2. Example [17] 2.3. Metrics for probability distributions [22] 2.4. Estimators seen as functionals of distributions [34] 3. Robustness, breakdown point and influence function [48] 3.1. Definition of robustness [48] 3.2. Definition of breakdown point [51] 3.3. The influence function [52] 4. The jackknife method [55] 4.1. Introduction [55] 4.2. The jackknife advanced theory [59] 4.3. Case study [72] 4.4. Comments [75] 5. Bootstrap methods, sampling distributions [78] 5.1. Bootstrap methods [78] 5.2. Sampling distribution of estimators [83] PART B 6. Type M estimators 90' 6.1. Definition [90] 6.2. Influence function and variance [92] 6.3. Robust M estimators [95] 6.4. Robustness, quasi-robustness and non-robustness [100] 6.4.1. Statement of the location problem [102] 6.4.2. Least powers [103] 6.4.3. Huber’s function [107] 6.4.4. Modification to Huber’s proposal [109] 6.4.5. Function ’’Fair’’ [110] 6.4.6. Cauchy’s function [111] 6.4.7. Welsch’s function [112] 6.4.8. "Bisquare" function [112] 6.4.9. Andrews’s function [113] 6.4.10. Selection of the p-function [113] 7. Type L estimators [117] 7.1. Definition [117] 7.2. Influence function and variance [120] 7.3. The median and related estimators [124] 8. Type R estimator [131] 8.1. Definition [131] 8.2. Influence function and variance [132] 9. Type MM estimators [134] 9.1. Definition [134] 9.2. Influence function and variance [136] 9.3. Linear model and robustness - Generalities [138] 9.4. Scale of residuals [143] 9.5. Robust linear regression [149] 9.6. Robust estimation of multivariate location and scatter [167] 9.7. Robust non-linear regression [172] 9.8. Numerical methods [178] 9.8.1. Relaxation methods [179] 9.8.2.,Simultaneous solutions [182] 9.8.3 Solution of fixed-point and non-linear equations [184] 10. Quantile estimators and confidence intervals [190] 10.1. Quantile estimators [190] 10.2. Confidence intervals [193] 11. Miscellaneous [196] 11.1. Outliers and their treatment [196] 11.2. Analysis of variance, constraints on minimization [199] 11.3. Adaptive estimators [202] 11.4. Recursive estimators [204] 11.5. Concluding remark [206] 12. References [207] 13. Subject index [234]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 R456 (Browse shelf) | Available | A-9365 |
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| 62 R215-2 Linear statistical inference and its applications / | 62 R215a Advanced statistical methods in biometric research / | 62 R215m Linear models : | 62 R456 Introduction to robust and quasi-robust statistical methods / | 62 R563 Mathematical statistics / | 62 R586 Métodos estadísticos / | 62 R589 Spatial statistics / |
Includes index.
Bibliografía: p. 207-233.
Table of contents --
1. Introduction and Summary [1] --
1.1. History and main contributions [1] --
1.2. Why robust estimations? [4] --
1.3. Summary [9] --
PART A --
The Theoretical Background --
2. Sample spaces, distributions, estimators [16] --
2.1. Introduction [16] --
2.2. Example [17] --
2.3. Metrics for probability distributions [22] --
2.4. Estimators seen as functionals of distributions [34] --
3. Robustness, breakdown point and influence function [48] --
3.1. Definition of robustness [48] --
3.2. Definition of breakdown point [51] --
3.3. The influence function [52] --
4. The jackknife method [55] --
4.1. Introduction [55] --
4.2. The jackknife advanced theory [59] --
4.3. Case study [72] --
4.4. Comments [75] --
5. Bootstrap methods, sampling distributions [78] --
5.1. Bootstrap methods [78] --
5.2. Sampling distribution of estimators [83] --
PART B --
6. Type M estimators 90' --
6.1. Definition [90] --
6.2. Influence function and variance [92] --
6.3. Robust M estimators [95] --
6.4. Robustness, quasi-robustness and non-robustness [100] --
6.4.1. Statement of the location problem [102] --
6.4.2. Least powers [103] --
6.4.3. Huber’s function [107] --
6.4.4. Modification to Huber’s proposal [109] --
6.4.5. Function ’’Fair’’ [110] --
6.4.6. Cauchy’s function [111] --
6.4.7. Welsch’s function [112] --
6.4.8. "Bisquare" function [112] --
6.4.9. Andrews’s function [113] --
6.4.10. Selection of the p-function [113] --
7. Type L estimators [117] --
7.1. Definition [117] --
7.2. Influence function and variance [120] --
7.3. The median and related estimators [124] --
8. Type R estimator [131] --
8.1. Definition [131] --
8.2. Influence function and variance [132] --
9. Type MM estimators [134] --
9.1. Definition [134] --
9.2. Influence function and variance [136] --
9.3. Linear model and robustness - Generalities [138] --
9.4. Scale of residuals [143] --
9.5. Robust linear regression [149] --
9.6. Robust estimation of multivariate location and scatter [167] --
9.7. Robust non-linear regression [172] --
9.8. Numerical methods [178] --
9.8.1. Relaxation methods [179] --
9.8.2.,Simultaneous solutions [182] --
9.8.3 Solution of fixed-point and non-linear equations [184] --
10. Quantile estimators and confidence intervals [190] --
10.1. Quantile estimators [190] --
10.2. Confidence intervals [193] --
11. Miscellaneous [196] --
11.1. Outliers and their treatment [196] --
11.2. Analysis of variance, constraints on minimization [199] --
11.3. Adaptive estimators [202] --
11.4. Recursive estimators [204] --
11.5. Concluding remark [206] --
12. References [207] --
13. Subject index [234] --
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