, Volume 81, Issue 6, pp 609–618 | Cite as

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

  • Ya. Yu. Nikitin


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.


Testing of normality U-statistics Bahadur efficiency Kolmogorov test 

Mathematics Subject Classification

62G10 62G20 



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

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interests.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Saint-Petersburg State UniversitySt. PetersburgRussia
  2. 2.Higher School of EconomicsNational Research UniversitySt. PetersburgRussia

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