Empirical bayes testing of a distribution function with d1richlet process priors

This paper considers the generalised empirical Bayes two-action (testing) and multiple action problems concerning a distribution function The Dirichiet process priors p of Ferguson have been used as the prior distributions on the space of distribution functions on the real line. The two-action component problem is considered in detail and when p is unknown partially empirical Bayes procedures {6 } which are asymptotically optimal with rates 0{jT1/2) and OCCmCn+l))     

An emprical bayes approach to two-sample problems with censored data

Empirical Bayes methods are used in estimating the probability based on randomly right-censored samples. The estimator is shown to be asymptotically optimal. Thus, in a way, this uork is similar to the results of Hollander and Korwar (1976) who used a similar approach in estimating A in the case of non-censored data. We also give hero a shorter proof to their rate result. In addition, a. resting procedure is obtained to test the hypothesis against on the basis of censored data. It is shown that this procedure is asymptotically optimal with rate of convergence n . Tnis result is analogous to our earlier result for the uncensored case (1970) The empirical Hayes procedure has been illustrated by means of a practical example.