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On asymptotic efficiency and deficiency of some adaptive tests in the one-sample problem

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Abstract

In this paper, we consider adaptive tests for the one-sample problem and investigate the order of difference between the power of a given adaptive asymptotically efficient test and that of the most powerful test. 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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References

  1. W. Albers, “Asymptotic expansions for the power of adaptive rank tests in the one-sample problem,”Lect. Notes Math.,821, 108–158 (1979).

    MathSciNet  Google Scholar 

  2. R. Beran, “Asymptotically efficient adaptive rank estimates in location models,”Ann. Statist.,2, 63–74 (1974).

    MATH  MathSciNet  Google Scholar 

  3. P. J. Bickel, D. M. Chibisov, and W. R. Van Zwet, “On efficiency of the first and second order,”Internat. Statist. Rev.,49, 169–175 (1981).

    MathSciNet  Google Scholar 

  4. D. M. Chibisov, “Asymptotic expansions and deficiencies of tests,” in:Proceedings of Internat. Congress of Math., Vol. 2, Warszawa (1983), pp. 1063–1079.

  5. J. Hájek and Z. Šidák,Theory of Rank Tests, Academic Press, New York (1967).

    Google Scholar 

  6. V. E. Bening, “A formula for deficiency: one sampleL- andR-tests. I,”Math. Meth. Statist.,44, No. 2, 167–188 (1995).

    MathSciNet  Google Scholar 

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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. 93-01-01446).

Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.

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Bening, V.E. On asymptotic efficiency and deficiency of some adaptive tests in the one-sample problem. J Math Sci 81, 2894–2899 (1996). https://doi.org/10.1007/BF02362499

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  • DOI: https://doi.org/10.1007/BF02362499

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