Characterization test for the multivariate skew-normal distribution with unknown parameters

Based on the characterization test for uniformity on the unit sphere surface, this paper proposes a characterization test for the multivariate skew-normal distribution. The test is constructed from the Moore-Penrose inverse and the canonical form of the multivariate skew-normal distribution, the test statistic can be easily computed for any dimension. Under the null hypothesis, the asymptotic uniform distribution of the transformed sample on the unit sphere surface is obtained. Several examples further illustrate the validity of the characterization test. Based on the parametric bootstrap method, an algorithm is given to estimate the p- value of the test statistic.