Tests for multivariate skew normal distributions based on the canonical form and the Shapiro–Wilk statistic

This manuscript addresses the problem of testing the multivariate skew normal distribution hypothesis when the parameter values are unknown. Data are transformed by using the canonical form of the MSN distribution and then the univariate skew-normality hypothesis is assessed with the Shapiro–Wilk test. Three tests based on statistics that summarize the marginal assessments are proposed. The size and power properties of the tests are estimated under different parameter configurations and alternative distributions in various dimensions by means of a Monte Carlo simulation study. The results show that the proposed tests are competitive against other existing tests for the same problem. A real data set is analyzed to illustrate the practical utility of the proposed methodologies. R scripts to implement the tests are available at a GitHub repository.