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Vanishing shortcoming of data driven Neyman's tests

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The shortcoming of a test is the difference between the power of the test and the power of the most powerful test. For a large set of alternatives converging to the null hypothesis asymptotic optimality of data driven Neyman's tests is shown in terms of vanishing shortcoming when the level of signicance tends to zero. In contrast to classical goodness-of-fit tests data driven Neyman's tests are asymptotically efficient in an infinite number of orthogonal directions.

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