Jackknifing, weighting, diagnostics and variance estimation in generalized M-estimation

We study and compare methods of covariance matrix estimation, and some diagnostic procedures, to accompany generalized ("Bounded Influence") M-estimation of regression in the linear model. The methods derive from one-step approximations to the delete-one estimates of the regression parameters. Two weighting schemes are also compared. The comparisons are made through a simulation study and a case study. The jackknife-based covariance estimates are successful at improving the coverages of associated confidence intervals; One of the weighting schemes is found to be quite generally superior to the other, with respect to mean-squared error and to confidence interval coverage, on data containing a realistic proportion of outliers and high leverage points. (C) 2000 Elsevier Science B.V. All rights reserved MSG: primary 62F35; 62J05; secondary 62J20.