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On the Bounded-Influence Regression Estimator of Krasker and Welsch

David Ruppert
Journal of the American Statistical Association
Vol. 80, No. 389 (Mar., 1985), pp. 205-208
DOI: 10.2307/2288073
Stable URL: http://www.jstor.org/stable/2288073
Page Count: 4
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On the Bounded-Influence Regression Estimator of Krasker and Welsch
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Abstract

Recently, Krasker and Welsch (1982) considered a class of bounded-influence regression estimators. They showed that within this class the so-called Krasker-Welsch estimator is the only solution to a first-order necessary condition for strong optimality, that is, for minimizing, in the sense of positive definiteness, the asymptotic covariance matrix. However, whether any strongly optimal estimator in fact exists remained an open question. In this article, an example is given where no strongly optimal estimator exists. Moreover, the practical significance of the lack of a strongly optimal estimator is discussed.

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