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A goodness-of-fit test for elliptical distributions with diagnostic capabilities

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  • Ducharme, Gilles R.
  • Lafaye de Micheaux, Pierre

Abstract

This paper develops a test of goodness-of-fit for elliptical distributions. The test is invariant to affine-linear transformations and has a convenient expression that can be broken into components containing diagnostic information to be used to identify possible departures when the test rejects. The test is developed for the bivariate Laplace, logistic and Pearson type II distributions, as well as the multivariate normal for which the R package ECGofTestDx is available on the CRAN. A simulation shows the usefulness of the diagnostic tools.

Suggested Citation

  • Ducharme, Gilles R. & Lafaye de Micheaux, Pierre, 2020. "A goodness-of-fit test for elliptical distributions with diagnostic capabilities," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:jmvana:v:178:y:2020:i:c:s0047259x19303720
    DOI: 10.1016/j.jmva.2020.104602
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    References listed on IDEAS

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    1. Gilles R. Ducharme & Walid Al Akhras, 2016. "Tree based diagnostic procedures following a smooth test of goodness-of-fit," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 971-989, November.
    2. 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.
    3. Boulerice, Bernard & Ducharme, Gilles R., 1997. "Smooth Tests of Goodness-of-Fit for Directional and Axial Data," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 154-175, January.
    4. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    5. 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.
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    Cited by:

    1. Makigusa, Natsumi & Naito, Kanta, 2020. "Asymptotics and practical aspects of testing normality with kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    3. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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