Most powerful conditional tests

Janssen Arnold and Völker Dominik

Statistics & Risk Modeling, 2007, vol. 25, issue 1, 41-62

Abstract: The present paper establishes finite sample most powerful tests for certain nonparametric null hypotheses P0 which admit a sufficient statistic S. The underlying alternatives are of semiparametric or nonparametric nature. Optimal one-sided S-conditional test are offered for families with nonparametric isotone likelihood ratio. Similarly two-sided optimal locally unbiased S-conditional test are introduced for alternatives with nonparametric convex likelihood. If in addition S is P0-complete then of course we arrive at most powerful α-similar tests. Special examples are randomization tests, permutation tests for two-sample problems and symmetry tests for the null hypothesis of 0-symmetry. The results rely on a new conditional Neyman–Pearson Lemma which can be found in the appendix and which is of own interest. This Lemma is used to solve conditional optimization problems for tests.

Keywords: conditional test; tests with Neyman-structure; conditional Neyman-Pearson Lemma; randomization test; permutation test; symmetry test; similar test; locally conditionally unbiased test; locally most powerful test (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1524/stnd.2007.25.1.41

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