Characterization Test for Multivariate Scale Mixtures of Skew- Normal Distributions

Based on the canonical form of multivariate scale mixtures of skew- normal (SMSN) distributions, a characterization test for multivariate SMSN distributions is proposed. The limiting null distribution of the transformed sample vectors is obtained and a simulation study is performed. Based on properties of spherical distributions and bootstrap approximation, an algorithm is given to estimate the critical values of the test statistic for the finite sample size. Moreover, a test statistic is constructed for testing skewness of the multivariate SMSN distributions.