Asymptotically Minimax Criteria for Testing Complex Nonparametric Hypotheses

Asymptotically minimax criteria are constructed for testing complex nonparametric hypotheses of symmetry, homogeneity, and independence. Here the sets of alternatives have a natural nonparametric representation. The traditional technique of reducing the problem to the corresponding problem for uniform distribution is not used in this study. At the same time, the specification of test statistics does not depend upon the hypothesis density.