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Local asympotic efficiency of some goodness-of-fit tests under skew alternatives

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  • Alessandra Durio
  • Yacov Yu. Nikitin

Abstract

The efficiency of most known distribution-free goodness-of-fitt tests such as Kolmogorov - Smirnov, Cramér - von Mises and their numerous variants was studied mainly under the classical alternatives of location and scale. However it is interesting to compare the efficiencies of these tests under asymmetric alternatives among which the most popular is the so-called skew alternative proposed by Azzalini (1985) in the case of the normal distribution. We find and compare local Bahadur efficiencies of many known statistics for skew alternatives and discuss also the conditions of their local optimality.

Suggested Citation

  • 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.
    • Handle: RePEc:icr:wpicer:04-2001
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    References listed on IDEAS

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    1. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    2. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
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    Cited by:

    1. 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.
    2. Henze, Norbert & Nikitin, Yakov & Ebner, Bruno, 2009. "Integral distribution-free statistics of Lp-type and their asymptotic comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3426-3438, July.
    3. 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.
    4. 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.
    5. Alessandra Durio & Yakov Nikitin, 2002. "Asympotic efficiency of signed - rank symmetry tests under skew alternatives," ICER Working Papers 12-2002, ICER - International Centre for Economic Research.
    6. Bojana Milošević & Marko Obradović, 2016. "Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 413-427, June.
    7. 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.

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