Abstract:

The paper studies the upper limit of possible contamination level which still allows to discriminate by a robust (likelihood ratio) test a hypothesis from an alternative. Having found this limit the test of a hypothesis against an alternative, both being increasingly contaminated with the increasing number of observations, are considered. The level of contamination is adjusted so that it allows discrimination with an a priori fixed risk. The asymptotic distribution of the test statistic is found and the tightness of approximation to the power of test based on this asymptotic distribution is illustrated by a small numerical example.