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Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization

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Abstract

We consider two scale-free tests of normality based on the characterization of the symmetric normal law by Ahsanullah et al. (Normal and student’s t-distributions and their applications, Springer, Berlin, 2014). Both tests have an U-empirical structure, but the first one is of integral type, while the second one is of Kolmogorov type. We discuss the limiting behavior of the test statistics and calculate their local exact Bahadur efficiency for location, skew and contamination alternatives.

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Acknowledgements

The author is thankful to the Editor, to the associate editor and two referees for careful reading of the manuscript, and some important remarks.

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Authors and Affiliations

  1. Saint-Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, Russia, 199034

    Ya. Yu. Nikitin

  2. Higher School of Economics, National Research University, Souza Pechatnikov, 16, St. Petersburg, Russia, 190008

    Ya. Yu. Nikitin

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  1. Ya. Yu. Nikitin
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Correspondence to Ya. Yu. Nikitin.

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The author declares that there is no conflict of interests.

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Supported by Grant RFBR 16-01-00258 and Grant SPbGU - DFG 6.65.37.2017.

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Nikitin, Y.Y. Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization. Metrika 81, 609–618 (2018). https://doi.org/10.1007/s00184-018-0673-0

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  • DOI: https://doi.org/10.1007/s00184-018-0673-0

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