Estimating the Standard Error of Robust Regression Estimates.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK DEPT OF STATISTICS
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Over the last two decades there has been much interest in the statistical literature in alternative methods to least squares for fitting equations to data. During this time a large number of estimates of regression coefficients have been proposed that are not unduly affected by a small percentage of the data so-called robust estimates. Although the robustness properties of these estimates have been studied in great detail, little attention has been paid to the problem of estimating the asymptotic covariance matrices of these estimates. Such estimates are necessary if inferences are to be made about the unknown regression parameters. This paper provides a brief description of two popular robust regression estimates, namely-M- and l sub 1 -estimates. It reviews the available methods for estimating the asymptotic covariance matrices of each of these estimates. In the case of M-estimates, it is shown how to use MINITAB to compute the robust estimates along with an estimated of their asymptotic covariance matrix. Finally, the different robust estimates and their estimated covariance matrices are compared via an example.
- Statistics and Probability