Minimum Distance Estimators of Scale with Censored Data

Abstract

Abstract This article examines how the level of censoring affects the performance of estimators of scale that minimize a weighted Cramervon Mises distance between the Kaplan-Meier product-limit estimator of the survival distribution function and an assumed model. The article shows that under certain conditions these estimators are asymptotically normal if the survival function is a member of the assumed scale family. Weights that minimize the asymptotic variance under these conditions also are found. Under stronger conditions, the minimum distance estimators (MDE's) are asymptotically normal even if the survival function is not a member of the assumed scale family. Asymptotic coverage probabilities of confidence intervals are found for percentiles constructed from exponential MDE's of scale under departures from the exponential distribution, and what happens in the limiting cases of no censoring and complete censoring is examined. Using the asymptotic results and Monte Carlo experiments, several exponenti...