VDR Conditional Tests for Multivariate Normality

The \chi^2 conditional test for multivariate normality is suggested. The transformed sample \mathbfY_d=R\mathbfV_d from a d-variate normal distribution has a symmetric multivariate Pearson type II distribution, the result that R^2 has a beta distribution is proved, the asymptotic Chi squared distribution of the statistic \chi^2 based on beta distribution and sphere uniform distribution is obtained. The Monte Carlo power study for multivariate normality suggests that our test is a powerful competitor to existing tests. The goodness-of-fit for multivariate normality of iris data is analyzed.