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Most powerful conditional tests

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  • Janssen Arnold
  • Völker Dominik

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.

Suggested Citation

  • Janssen Arnold & Völker Dominik, 2007. "Most powerful conditional tests," Statistics & Risk Modeling, De Gruyter, vol. 25(1), pages 41-62, January.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:1/2007:p:22:n:3
    DOI: 10.1524/stnd.2007.25.1.41
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    References listed on IDEAS

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    1. Arnold Janssen & Claus‐Dieter Mayer, 2001. "Conditional Studentized Survival Tests for Randomly Censored Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 283-293, June.
    2. Janssen, Arnold, 1997. "Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 9-21, November.
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    Cited by:

    1. Davide Di Cecco, 2012. "Conditional exact tests for Markovianity and reversibility in multiple categorical sequences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 170-187, March.

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