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.