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Flexible asymmetric multivariate distributions based on two-piece univariate distributions

Author

Listed:
  • Jonas Baillien

    (KU Leuven)

  • Irène Gijbels

    (KU Leuven)

  • Anneleen Verhasselt

    (Hasselt University)

Abstract

Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions, grouped under the name “skewed distributions”, have been developed to specifically cope with asymmetric data. In this paper, we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These are members of a flexible family of univariate asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are supported by a simulation study confirming the developed theoretical results, and some data examples to illustrate practical applicability.

Suggested Citation

  • Jonas Baillien & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible asymmetric multivariate distributions based on two-piece univariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 159-200, February.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:1:d:10.1007_s10463-022-00842-6
    DOI: 10.1007/s10463-022-00842-6
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    References listed on IDEAS

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    1. Francisco Louzada & Anderson Ara & Guilherme Fernandes, 2017. "The bivariate alpha-skew-normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7147-7156, July.
    2. Bindu Punathumparambath, 2012. "The multivariate asymmetric slash Laplace distribution and its applications," Statistica, Department of Statistics, University of Bologna, vol. 72(2), pages 235-249.
    3. Ley, Christophe & Paindaveine, Davy, 2010. "Multivariate skewing mechanisms: A unified perspective based on the transformation approach," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1685-1694, December.
    4. Struyf, Anja J. & Rousseeuw, Peter J., 1999. "Halfspace Depth and Regression Depth Characterize the Empirical Distribution," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 135-153, April.
    5. Kollo, Tõnu, 2008. "Multivariate skewness and kurtosis measures with an application in ICA," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2328-2338, November.
    6. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2006. "Families of Multivariate Distributions Involving the Rosenblatt Construction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1652-1662, December.
    7. M.C. Jones, 2016. "On bivariate transformation of scale distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 577-588, February.
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