ASYMPTOTICALLY OPTIMAL STATISTICS IN SOME MODELS WITH INCREASING FAILURE RATE AVERAGES
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Let F and G be defined by Ft Hgamma t and Gt Htheta t where H is unknown and HO 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.
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