Invariant tests for multivariate normality: a critical review

This paper gives a synopsis on affine invariant tests of the hypothesis that the unknown distribution of a d-dimensional random vector X is some nondegenerate d-variate normal distribution, on the basis of i.i.d. copies X$_1$,...,X$_n$ of X. Particular emphasis is given to progress that has been achieved during the last decade. Furthermore, we stress the typical diagnostic pitfall connected with purportedly ‘directed’ procedures, such as tests based on measures of multivariate skewness.