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

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  • Tenreiro, Carlos

Abstract

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.

Suggested Citation

  • Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1038-1053
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    References listed on IDEAS

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    Cited by:

    1. Ebner, Bruno, 2012. "Asymptotic theory for the test for multivariate normality by Cox and Small," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 368-379.
    2. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0680-4 is not listed on IDEAS
    3. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    4. Simos G. Meintanis & James Allison & Leonard Santana, 2016. "Goodness-of-fit tests for semiparametric and parametric hypotheses based on the probability weighted empirical characteristic function," Statistical Papers, Springer, vol. 57(4), pages 957-976, December.
    5. repec:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0288-1 is not listed on IDEAS
    6. Christian Goldmann & Bernhard Klar & Simos Meintanis, 2015. "Data transformations and goodness-of-fit tests for type-II right censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 59-83, January.
    7. Meintanis, Simos G. & Tsionas, Efthimios, 2010. "Testing for the generalized normal-Laplace distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3174-3180, December.
    8. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    9. repec:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0544-4 is not listed on IDEAS
    10. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    11. N. Balakrishnan & M. Brito & A. Quiroz, 2013. "On the goodness-of-fit procedure for normality based on the empirical characteristic function for ranked set sampling data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 161-177, February.
    12. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos Meintanis, 2012. "Monitoring changes in the error distribution of autoregressive models based on Fourier methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 605-634, December.

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