Abstract
The robust regression estimators of Huber and Welsch and the bounded influence estimators of Krasker and Welsch require the specification of a cut-off or tuning constant before they are fully defined. Here the asymptotic mean squared errors of these estimators under different designs/distributions for the explanatory variables and different error distribution are computed. The choice of tuning constants seems to be critical in the trade-off between bias and variance. The choice illuminates the differences in behaviour of the estimators. Rousseeuw's least median of squares estimator is also considered. Two numerical examples further illustrate the differences.
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