ON ROBUSTNESS FOR HYPOTHESES TESTING

A way to deal with robustness in hypotheses testing using a tail-order ing on distributions is described. We prove, under mild conditions tha t to test H-0: theta less-than-or-equal-to theta0 against H-1: theta > theta0 at level alpha < 0.5, the uniformly most powerful (UMP) test t hat accepts H-0 when X has distribution function F(X squiggly arrow po inting right F) would also accept this with X squiggly arrow pointing right G if F <t G. Likewise, the UMP test that rejects H-0 with X squi ggly arrow pointing right F would also reject it with X squiggly arrow pointing right D if D <t F, where <t is the tail-ordering defined by Loh (1984), and where F, G and D belong to the class of distributions F defined below. For distributions of this class we define the r-valu e as a measure of test robustness against changes in the model distrib ution. We also make an analysis of test robustness using the asymptoti c distribution of the random variable p-value.