Assessing Multivariate Normality on the "Worst" Sample Configuration

A rotation procedure searching for the worst sample configuration is proposed when the hypothesis of multivariate normality is assessed by evaluating the univariate normality of each row of the scaled residual matrix.This procedure gives rise to multivariate normality test statistics which are invariant with respect to linear non-singular transformations of the sample data. An empirical power study with respect to selected alternative distributions demonstrates how the worst rotation procedure performs better than the rotation procedure proposed by Szkutnik.