EMPIRICAL BAYES APPROACH TO 2-SAMPLE PROBLEMS WITH CENSORED DATA

Empirical Bayes methods are used in estimating the probability A = P(X <Y) based on randomly right-censored samples. The estimator is shown to be asymptotically optimal. Thus, in a way, this work is similar to the results of Hollander and Korwar (1976) who used a similar approach in estimating A in the case of noncensored data. We also give here a shorter proof to their rate result. In addition, a testing procedure is obtained to test the hypothesis h0:f < G against H0:E G on the basis of censored data. It is shown that this procedure is asymptotically optimal with rate of convergence n. This result is analogous to our earlier result for the uncensored case (1976). The empirical Bayes procedure has been illustrated by means of a practical example. © 1979, Taylor & Francis Group, LLC. All rights reserved.