Sequential estimation of the mean survival time under random censorship

Abstract

The paper considers the problem of sequential estimation of the mean survival time using randomly right censored data when the loss is measured by the sum of the squared error of estimation and the cost of observations made with per unit cost c being constant. The sequential estimator defined here is shown to be asymptotically risk efficient and asymptotically normal as c 4 ↓ 0 under certain regularity conditions. These conditions are shown to be satisfied by a wide variety of survival distributions and censoring distributions. Furthermore, they hold trivially when the mean survival experience over a finite interval [0,T], T < ∞, is of interest.