Asymptotics of Generalized S-Estimators

✍ Scribed by O. Hossjer; C. Croux; P.J. Rousseeuw

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 804 KB
• Volume: 51
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1994.1055

✦ Synopsis

An (S)-estimator of regression is obtained by minimizing an (M)-estimator of scale applied to the residuals (r_{i}). On the other hand, a generalized (S)-estimator (or (G S) estimator) minimizes an (M)-estimator of scale based on all pairwise differences (r_{i}-r_{j}). Generalized (S)-estimators have similar robustness properties as (S)-estimators, including a high breakdown point. In this paper we prove asymptotic normality for the (G S)-esimator of the regression parameters, as well as for the accompanying scale estimator defined by the minimal value of the objective function. It turns out that the asymptotic efficiency can be much higher than that of (S)-estimators. For instance, by using a biweight (\rho)-function we obtain a GS-estimator with (50 %) breakdown point and (68.4 %) efficiency. 1994 Academic Press, Inc.