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On the power of some adaptive tests in the one-sample problem

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Abstract

In this paper, we study adaptive tests for the one-sample problem. The limit of the normalized difference between the power of a given adaptive test and that of the most powerful test is found. This limit directly yields the Hodges-Lehmann asymptotic deficiency of corresponding adaptive tests. Here adaptation means that the efficient score function of the test is estimated from the sample. A Fourier series estimator is used for the score function.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Vorob'yovy Gory, 119899, Moscow, Russia

    V. E. Bening

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  1. V. E. Bening
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Additional information

Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-1446).

Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.

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Bening, V.E. On the power of some adaptive tests in the one-sample problem. J Math Sci 89, 1468–1485 (1998). https://doi.org/10.1007/BF02362282

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  • DOI: https://doi.org/10.1007/BF02362282

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