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On the choice of the smoothing parameter for the BHEP goodness-of-fit test

  • Tenreiro, Carlos
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    The BHEP (Baringhaus-Henze-Epps-Pulley) test for assessing univariate and multivariate normality has shown itself to be a relevant test procedure, recommended in some recent comparative studies. It is well known that the finite sample behaviour of the BHEP goodness-of-fit test strongly depends on the choice of a smoothing parameter h. A theoretical and finite sample based description of the role played by the smoothing parameter in the detection of departures from the null hypothesis of normality is given. Additionally, the results of a Monte Carlo study are reported in order to propose an easy-to-use rule for choosing h. In the important multivariate case, and contrary to the usual choice of h, the BHEP test with the proposed smoothing parameter presents a comparatively good performance against a wide range of alternative distributions. In practice, if no relevant information about the tail of the alternatives is available, the use of this new bandwidth is strongly recommended. Otherwise, new choices of h which are suitable for short tailed and long tailed alternative distributions are also proposed.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4TCR1JD-2/2/e3273c9b1d9f17ba7628158a1ca5b9f9
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 4 (February)
    Pages: 1038-1053

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1038-1053
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
    2. Sándor Csörgő, 1989. "Consistency of some tests for multivariate normality," Metrika, Springer, vol. 36(1), pages 107-116, December.
    3. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika, Springer, vol. 35(1), pages 339-348, December.
    4. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
    5. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    6. 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.
    7. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    8. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
    9. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    10. Henze, Norbert, 1997. "Extreme smoothing and testing for multivariate normality," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 203-213, October.
    11. Arcones, Miguel A. & Wang, Yishi, 2006. "Some new tests for normality based on U-processes," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 69-82, January.
    12. Gouriéroux, Christian & Tenreiro, Carlos, 2001. "Local Power Properties of Kernel Based Goodness of Fit Tests," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 161-190, August.
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