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Shapiro-Wilk test for multivariate skew-normality

Author

Listed:
  • Elizabeth González-Estrada

    (Colegio de Postgraduados)

  • José A. Villaseñor

    (Colegio de Postgraduados)

  • Rocío Acosta-Pech

    (Colegio de Postgraduados)

Abstract

The multivariate skew-normal family of distributions is a flexible class of probability models that includes the multivariate normal distribution as a special case. Two procedures for testing that a multivariate random sample comes from the multivariate skew-normal distribution are proposed here based on the estimated canonical form. Canonical data are transformed into approximately multivariate normal observations and then a multivariate version of the Shapiro-Wilk test is used for testing multivariate normality. Critical values for the tests are approximated without using parametric bootstrap. Monte Carlo simulation results provide evidence that the nominal test level is preserved, in general, under the considered settings. The simulation results also indicate that these tests are in general more powerful than existing tests for the same problem versus the studied alternatives.

Suggested Citation

  • Elizabeth González-Estrada & José A. Villaseñor & Rocío Acosta-Pech, 2022. "Shapiro-Wilk test for multivariate skew-normality," Computational Statistics, Springer, vol. 37(4), pages 1985-2001, September.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01188-y
    DOI: 10.1007/s00180-021-01188-y
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    References listed on IDEAS

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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Simos G. Meintanis & Zdeněk Hlávka, 2010. "Goodness‐of‐Fit Tests for Bivariate and Multivariate Skew‐Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 701-714, December.
    3. Balakrishnan, N. & Capitanio, A. & Scarpa, B., 2014. "A test for multivariate skew-normality based on its canonical form," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 19-32.
    4. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
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