Smooth Test for Multivariate Skew-Normality

Abstract

Based on the smooth test for uniformity on the surface of a unit sphere, a new test for multivariate skew-normality is presented. The asymptotic null distribution of the transformed sample is obtained, and a bootstrapping algorithm is given to estimate the p-value of the test statistic. By using the Anderson-Darling test, a bootstrapping procedure is provided in order to test whether the shape parameter is zero in the multivariate skew-normal distribution.