Shapiro-Wilk test for multivariate skew-normality

• Published in: Computational statistics Vol. 37; no. 4; pp. 1985 - 2001
• Main Authors: González-Estrada, Elizabeth, Villaseñor, José A., Acosta-Pech, Rocío
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022; Springer Nature B.V
• Subjects: Canonical forms; Economic Theory/Quantitative Economics/Mathematical Methods; Hypotheses; Mathematics and Statistics; Monte Carlo simulation; Multivariate analysis; Normal distribution; Normality; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Random variables; Skewed distributions; Statistical analysis; Statistics; Skew distributions; Multivariate normality tests; Multivariate data; Goodness-of-fit; Monte Carlo simulation
• DOI: 10.1007/s00180-021-01188-y
• ISSN: 0943-4062

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.