The iteratively reweighted estimating equation in minimum distance problems

Abstract

The class of density based minimum distance estimators provide attractive alternatives to the maximum likelihood estimator because several members of this class have nice robustness properties while being first-order efficient under the assumed model. A helpful computational technique—similar to the iteratively reweighted least squares used in robust regression—is introduced which makes these estimators computationally much more feasible. This technique is much simpler than the Newton–Raphson ( NR) method to implement. The loss suffered in the rate of convergence compared to the NR method can be made to vanish in some exponential family situations by a little modification in the weight function—in which case the performance is comparable to the NR method. For a large number of parameters the performance of this modified version is actually expected to be better than the NR method. In view of the widespread interest in density based robust procedures, this modification appears to be of great practical value.