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Lilliefors test for exponentiality: Large deviations, asymptotic efficiency, and conditions of local optimality

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Abstract

We study large deviations and Bahadur efficiency of the Lilliefors statistic for testing of exponentiality. This statistic belongs to the class of Kolmogorov-Smirnov type statistics with estimated parameters. Large deviation asymptotics of such statistic is found for the first time. We show that the test has relatively high local efficiency and construct the alternative for which it is locally optimal.

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Authors and Affiliations

  1. Dept. of Math. and Mech. and School of Management, St. Petersburg State University, Universitetski pr., 28, St. Petersburg, 198504, Russia

    Ya. Yu. Nikitin

  2. St. Petersburg Electrotechnical University, Prof. Popova str. 5, St. Petersburg, 197376, Russia

    A. V. Tchirina

Authors
  1. Ya. Yu. Nikitin
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  2. A. V. Tchirina
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Nikitin, Y.Y., Tchirina, A.V. Lilliefors test for exponentiality: Large deviations, asymptotic efficiency, and conditions of local optimality. Math. Meth. Stat. 16, 16–24 (2007). https://doi.org/10.3103/S1066530707010024

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  • DOI: https://doi.org/10.3103/S1066530707010024

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