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A new powerful version of the BUS test of normality

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  • Aldo Goia
  • Ernesto Salinelli
  • Pascal Sarda

Abstract

In this paper we introduce a modified version of the BUS test, which we call NBUS (New Borovkov–Utev Statistic). This latter defines a family of goodness of fit tests that can be used to detect normality against alternative hypothesis of which all moments up to the fifth exist. The test statistic depends on empirical moments and real parameters that have to be chosen appropriately. The good abilities of the NBUS with respect to BUS and other powerful normality tests are illustrated by means of a Monte Carlo experiment for finite samples. Besides, we show how an adaptation of NBUS for testing departing from normality due only to kurtosis, leads to comparable performances with classical tests based on the fourth moment. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2015. "A new powerful version of the BUS test of normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 449-474, September.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:3:p:449-474
    DOI: 10.1007/s10260-014-0292-5
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    References listed on IDEAS

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    1. Bonett, Douglas G. & Seier, Edith, 2002. "A test of normality with high uniform power," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 435-445, September.
    2. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    3. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    4. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    5. Urzua, Carlos M., 1996. "On the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 53(3), pages 247-251, December.
    6. Poitras, Geoffrey, 2006. "More on the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 90(3), pages 304-309, March.
    7. Wei Ning & Grace Ngunkeng, 2013. "An empirical likelihood ratio based goodness-of-fit test for skew normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 209-226, June.
    8. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2011. "Exploring the statistical applicability of the Poincaré inequality: a test of normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 334-352, August.
    9. Carota, Cinzia, 2010. "Tests for normality in classes of skew-t alternatives," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 1-8, January.
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    Cited by:

    1. Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.

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