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

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  • Ya. Yu. Nikitin

    (Saint-Petersburg State University
    National Research University)

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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  • Ya. Yu. Nikitin, 2018. "Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 609-618, August.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:6:d:10.1007_s00184-018-0673-0
    DOI: 10.1007/s00184-018-0673-0
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    References listed on IDEAS

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    1. Durio, A. & Nikitin, Ya.Yu., 2016. "Local efficiency of integrated goodness-of-fit tests under skew alternatives," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 136-143.
    2. Bera, Anil K. & Galvao, Antonio F. & Wang, Liang & Xiao, Zhijie, 2016. "A New Characterization Of The Normal Distribution And Test For Normality," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1216-1252, October.
    3. Ya. Nikitin, 2010. "Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 649-668.
    4. Alessandra Durio & Yacov Yu. Nikitin, 2001. "Local asympotic efficiency of some goodness-of-fit tests under skew alternatives," ICER Working Papers 04-2001, ICER - International Centre for Economic Research.
    5. Pietro Muliere & Yakov Nikitin, 2002. "Scale-invariant test of normality based on Polya's characterization," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 20-32.
    6. Yakov Y. Nikitin & Irina Peaucelle, 2004. "Efficiency and local optimality of nonparametric tests based on U- and V-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 185-200.
    7. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
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