Asymptotically Optimal Statistics in Some Models with Increasing Failure Rate Averages

Abstract

Abstract : Let F and G be defined by F(t) = H(gamma t) and G(t) = H(theta t) where H is unknown and H(O) = O. For testing the equality of the means of F and G in the two-sample problem; it is shown that the Savage (The Annals of Mathematical Statistics (1956) pp 590-615) statistic maximizes the minimum power over increasing failure rate distributions asymptotically. Asymptotic uniqueness holds only in a class of rank tests. The results are extended to censored samples, the problem of estimating the ratio of the means, and the k-sample problem.