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Robust regression by means of S-estimators. (English) Zbl 0567.62027

Robust and nonlinear time series analysis, Proc. Workshop, Heidelberg/Ger. 1983, Lect. Notes Stat., Springer-Verlag 26, 256-272 (1984).
[For the entire collection see Zbl 0553.00008.]
In this paper the authors develop a class of methods for robust regression and briefly comment on their use in time series. These new estimators are introduced because of their invulnerability to large fractions of contaminated data. The authors propose to call them ”S- estimators” because they are based on estimators of \b{s}cale. In the following the finite-sample version of the breakdown point is used as a quantitative measure of robustness.
In the first part a survey on different estimators for the regression parameter is given and their robustness properties are compared with respect to the breakdown point, affine equivariance and velocity of convergence. The S-estimator of the regression parameter is introduced.
In the second part the breakdown point of the S-estimator is determined; it tends to 50% when the sample size n becomes large. In the third part two numerical examples are given to demonstrate the usefulness of S- estimators, one example with a large fraction of outliers.
In the fourth part the asymptotic behaviour of S-estimators, i.e. consistency, asymptotic normality, and efficiency, is investigated. Finally, in the fifth part, some general remarks on the computation of S- estimators are made and generalizations of S-estimators are indicated.
Reviewer: H.Büning

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05 Linear regression; mixed models

Citations:

Zbl 0553.00008