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Bahadur efficiency and local optimality of a test for exponentiality based on the Moran statistics

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Abstract

We study the scale-free test for exponentiality introduced by Moran. This test has been constructed as an optimal test of exponentiality against the gamma alternatives but it also may be used to test exponentiality against the IFR and DFR classes of alternatives. We obtain rough large deviation asymptotics of the test under the null hypothesis and find its Bahadur efficiency values for most commonly used alternatives to exponentiality. We also describe the local Bahadur optimality domain of the test. The large deviations theorem describes as well the asymptotic behavior of a spacings-based Darling test for uniformity under the null hypothesis. Bibliography: 9 titles.

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg

    A. V. Tchirina

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  1. A. V. Tchirina
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 245–259.

The author is heartily grateful to Prof. Ya. Yu. Nikitin for advices and comments concerning this paper.

This research was supported by the Russian Fundation for Basic Research, grant 00-15-96019.

Translated by A. V. Tchirina.

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Tchirina, A.V. Bahadur efficiency and local optimality of a test for exponentiality based on the Moran statistics. J Math Sci 127, 1812–1819 (2005). https://doi.org/10.1007/s10958-005-0143-x

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  • DOI: https://doi.org/10.1007/s10958-005-0143-x

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