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Bahadur Efficiency of EDF Based Normality Tests when Parameters are Estimated

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In the present paper, some well-known tests based on empirical distribution functions (EDF) with estimated parameters for testing composite normality hypothesis are revisited, and some new results on asymptotic properties are provided. In particular, the approximate Bahadur slopes are obtained in the case of close alternatives for the EDF-based tests as well as the likelihood ratio test. The local approximate efficiencies are calculated for several close alternatives. The obtained results could serve as a benchmark for evaluation of the quality of recent and future normality tests.

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Authors and Affiliations

  1. University of Belgrade, Faculty of Mathematics, Belgrade, Serbia

    B. Milošević & M. Obradović

  2. St. Petersburg State University, St. Petersburg, Russia

    Ya. Yu. Nikitin

Authors
  1. B. Milošević
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  2. Ya. Yu. Nikitin
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  3. M. Obradović
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Corresponding authors

Correspondence to B. Milošević or M. Obradović.

Additional information

Ya. Yu. Nikitin is deceased.

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 501, 2021, pp. 203–217.

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Milošević, B., Nikitin, Y.Y. & Obradović, M. Bahadur Efficiency of EDF Based Normality Tests when Parameters are Estimated. J Math Sci 273, 793–803 (2023). https://doi.org/10.1007/s10958-023-06542-7

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  • DOI: https://doi.org/10.1007/s10958-023-06542-7

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