Minimax Results for IFRA Scale Alternatives
Abstract : Let X sub 1, ..., X sub m and Y sub 1, ..., Y sub n be two independent random samples from populations with continuous IFRA distributions F(.) and F(./delta) respectively, and let s sub 1, ..., s sub n denote the ranks of the Y's in the combined sample. For testing H sub o: delta = or 1 vs. H sub 1 delta 1 it is shown that the error probabilities of each monotone rank test phi are bounded by the error probabilities for exponential alternatives. Inequalities are used to derive tests that maximize the minimum power in the class of all rank tests. The results are extended to censored samples, sequential sampling, distributions ordered by skewness, the problem of combining independent test statistics, and the goodness of fit problem.