Two simple resistant regression estimators with OP(n−1/2) convergence rate are presented. Ellipsoidal trimming can be used to trim the cases corresponding to predictor variables x with large Mahalanobis distances, and the forward response plot of the residuals versus the fitted values can be used to detect outliers. The first estimator uses ten forward response plots corresponding to ten different trimming proportions, and the final estimator corresponds to the “best” forward response plot. The second estimator is similar to the elemental resampling algorithm, but sets of O(n) cases are used instead of randomly selected elemental sets.
These two estimators should be regarded as new tools for outlier detection rather than as replacements for existing methods. Outliers should always be examined to see if they follow a pattern, are recording errors, or if they could be explained adequately by an alternative model. Using scatterplot matrices of fitted values and residuals from several resistant estimators is a very useful method for comparing the different estimators and for checking the assumptions of the regression model.