Weighted L2 quantile distance estimators for randomly censored data

Abstract

The asymptotic properties of a family of minimum quantile distance estimators for randomly censored data sets are considered. These procedures produce an estimator of the parameter vector that minimizes a weighted L 2 distance measure between the Kaplan-Meier quantile function and an assumed parametric family of quantile functions. Regularity conditions are provided which insure that these estimators are consistent and asymptotically normal. An optimal weight function is derived for single parameter families, which, for location/scale families, results in censored sample analogs of estimators such as those suggested by Parzen.