The scaled α-Winsorized estimate of exponential scale for censored data: an analysis based on two influence functions

Abstract

A new view of the maximum likelihood estimator (MLE) of exponential scale for censored data is presented. This is done by adapting Reid's (Ann. Statist. 9 (1981) 78) approach for obtaining the two influence functions (IF) for the Kaplan–Meier estimate of the survival function; one for uncensored and one for censored data, respectively. The MLEs two IFs are derived. Via this analysis, we propose a new robust estimator, the scaled α-Winsorized estimator (WE). Under Type II censoring, the WE is the MLE and, hence, is asymptotically efficient in that case. Its two IFs are bounded; hence,WE is B-robust. Its breakdown point is α. A comparison is made with respect to asymptotic bias and mean square error at contaminated exponential and Weibull survival models.