Asymptotic optimality of data-driven Neyman's tests for uniformity

Abstract

Data-driven Neyman's tests resulting from a combination of eyman' smooth tests for uniformity and Schwarz's selection procedure are nvestigated. Asymptotic intermediate efficiency of those tests with respect to the Neyman-Pearson test is shown to be 1 for a large set of converging alternatives. The result shows that data-driven Neyman's tests, contrary to classical goodness-of-it tests, are indeed omnibus tests adapting well to the data at hand.