LARGE SAMPLE THEORY FOR AN ESTIMATOR OF THE MEAN SURVIVAL TIME FROM CENSORED SAMPLES

This paper introduces and studies the large sample properties of an estimator for the mean survival time from censored samples. Let X,,...,X, be independent identically distributed random variables with F(x) = P[X,> x]. Let Y,,...,Yn be independent identically distributed (and independent of XI,...,Xn) censoring times with G(y) = P[Y,>y]. Based on observing only Zi = min(Xi, Y,) and which observations are censored (i.e., Xi> Y,), we give a class of estimators of the pean survival time p = Scflx)dx; The estimators are of the form i = S P F ( x) d x, where M,f rn as n t r n and F is an estimator of F depending on the Zi's and the censoring pattern. Conditions of F, G and {M,) for the asymptotic normality of are stated and proved in Section 2 based on approximations detailed in Section 3. Section 4 gives conditions for strong consistency of i with rates, while Section 5 examines the meaning of the conditions for the case of the negative exponential distributions for F and G. 1. Introduction and formulation of the problem. Let XI,