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Algorithms, routines, and \(S\) functions for robust statistics. The FORTRAN library ROBETH with an interface to S-PLUS. With the collaboration of Johann Joss and Alex Randriamiharisoa. (English) Zbl 0777.62004

Wadsworth & Brooks/Cole Statistics/Probability Series. Pacific Grove, CA: Wadsworth & Brooks / Cole Advanced Books & Software. xii, 436 p. (1993).
During the past two decades an important theoretical effort has been put into developing statistical procedures that are resistant to outliers and stable with respect to deviations from the given distributional model, so called robust procedures. Some of these methods have been implemented in different statistical programs and packages like BMDP, ISP, MINITAB, \(S+\), SAS, SPSS etc. Unfortunately they are neither complete nor (usually) complemented by appropriate inference procedures. Therefore, for several years a joint effort of the statistical group at the ETH Zürich and University of Lausanne has been aimed at filling the gap between theory and implementation. To this end many numerical algorithms have been developed and implemented into the FORTRAN subroutine library ROBETH, being a systematized collection of algorithms that allows the computation of a broad class of procedures based on \(M\)-estimation and high breakdown estimation, including robust regression, robust testing of linear hypotheses and robust covariances. On the other hand, many other robust procedures proposed in the literature like \(L\)- or \(R\)-estimates as well as related inference based on them are not covered.
The book itself describes the computational procedures included in ROBETH. Each chapter, with a few exceptions, consists of three parts, providing the reader with an overview of the theoretical background for the statistical and numerical methods, detailed description of the corresponding FORTRAN subroutines and of the numerical algorithms as they are implemented, and the script of several examples concerning the use of ROBETH by means of the \(S+\) interface, including some examples of high- level \(S\)-functions.
It should be stressed that the theoretical sections are concise and do not replace main references given at the beginning of each chapter. On the contrary, the emphasis is not on the theory but on the actual implementation. Moreover, the book does not introduce the use of \(S+\) and does not document in detail the \(S\)-functions based on ROBETH that are made available by the interface. Finally, the examples are not designed to compare and discuss the statistical methods but just to show how to use the software.
The book is accompanied by a 3 1/2 ” inch diskette (MS-DOS format) containing the sources of ROBETH and \(S+\) interface and several program examples with the corresponding data and results. The diskette does not form part of the book, but can be obtained for 30 SF directly from the author.
Contents: 1. Location problems. 2. \(M\)-estimates of coefficients and scale in linear regression. 3. Weights for bounded influence regression. 4. Covariance matrix of the coefficient estimates. 5. Asymptotic matrix of the coefficient estimates. 6. Robust testing in linear models. 7. High breakdown point regression. 8. \(M\)-estimates of covariance matrices. 9. Mixed procedures. 10. \(M\)-estimates for discrete generalized linear models. 11. Weight functions. 12. Utility routines. 13. FORTRAN sources. 14. \(S+\) interface.
Appendix 1: High-level routines for bounded influence regression. Appendix 2 : List of all subroutines. References. Index.
Reviewer: J.Antoch (Praha)

MSC:

62-04 Software, source code, etc. for problems pertaining to statistics
62F35 Robustness and adaptive procedures (parametric inference)
65C99 Probabilistic methods, stochastic differential equations
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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