On asymptotic admissibility of goodness-of-fit tests

Asymptotic properties of goodness-of-fit tests for testing simple and composite parametric hypotheses with continual alternatives are studied. The author investigates conditions under which goodness-of-fit tests are asymptotically admissible. He considers the question of completeness of the class of asymptotically admissible goodness-of-fit tests. To solve these problems he studies the properties of admissible tests for the limit problem of testing the hypothesis about the mean of a Gaussian random element in Hilbert space. As an application of the results he proves asymptotic admissibility and nonadmissibility of various goodness-of-fit tests used in practice.
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