On minimum distance estimation in two-sample scale problem with right censoring

Abstract

This paper considers some Koul and Yang (1989) type minimum L₂-distance estimators of the scale parameter, under the Koziol-Green (K-G) sub-model of the censored two-sample scale model. The specific forms of the pertinent distribution functions are not required and the use of the L₂-distance results in robust scale estimation. In our minimum L₂-distance estimator, the maximum likelihood estimator (MLE) for the survival function under the K-G model is used rather than the product limit estimator (PLE) of Kaplan and Meier (1958) that is used in Koul and Yang (1989). Several asymptotic properties of the estimator are established. A representation of the estimator that facilitates its computation is derived. Furthermore, it is shown that the minimum L₂-distance estimator based on the MLE of the survival function is asymptotically more efficient than the estimator based on the PLE of the survival function under the specified K-G sub-model.