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.
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Notes
The script for implementing this test in R (R Core Team 2021) is available from the authors.
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Acknowledgements
The authors are grateful to two anonymous reviewers for their constructive comments and suggestions on the original manuscript, which helped to improve notably the current version. The authors also thank Blanca Monroy-Castillo for useful discussions.
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González-Estrada, E., Villaseñor, J.A. & Acosta-Pech, R. Shapiro-Wilk test for multivariate skew-normality. Comput Stat 37, 1985–2001 (2022). https://doi.org/10.1007/s00180-021-01188-y
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DOI: https://doi.org/10.1007/s00180-021-01188-y