Configural polysampling techniques are an effective small sample method for studying and improving robust estimates for the (simple) regression problem. Attention is restricted to estimators which are regression-and-scale invariant. This restriction enables us to calculate the Pitman (optimal) estimator and its variance for distributions of interest. The nine distributions included in this study belong to the family of distributions called p-wild Gaussians. The Pitman estimator provides a standard by which to compare and assess the performance of other regression-and-scale invariant estimators, in particular M-estimators. Tukey's biweight estimator was examined in detail and calculated by iteratively reweighted least squares for various tuning constants, x-space designs, and initial starting estimators. The median absolute deviate (MAD) was used as a scale estimate in conjunction with the tuning constants c = 5, 6, 6.5, 7, 7.5, 8, 9, 10, 11, and 12. Eight symmetrical x-space designs were examined for sample size 20 and four symmetrical x-space designs were examined for sample size 10. The designs were chosen such that some of them contained leverage points and others did not. Least squares, least absolute deviations, and a modified version of the three group resistant line were used as the initial estimators in the iterative reweighted least squares computations. Numerous tables are presented containing the efficiency of the biweight estimator for the various distributions and x-space designs studied. Finally, polyeffective estimators defined by a minimax criterion are shown to be highly efficient.
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