Introduction to robust and quasi-robust statistical methods / William J.J. Rey.

Por: Rey, William J. J, 1940-Series UniversitextEditor: Berlin ; New York : Springer-Verlag, 1983Descripción: ix, 236 p. : ill. ; 25 cmISBN: 0387128662 (U.S. : pbk.)Tema(s): Robust statisticsOtra clasificación: *CODIGO*
Contenidos:
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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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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