Invariant tests for multivariate normality: A critical review

Henze, Norbert

facul_01; 16

Abstract:
This paper gives a synopsis of 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
skewness and kurtosis.

Primary MSC: 62G10 Hypothesis testing
Secondary MSC: 62F05 Asymptotic properties of tests
Keywords: Tests for multivariate normality, affine invariance, consistency, multivariate skewness, multivariate kurtosis, Roy's union-intersection principle, empirical characteristic function, angles and radii, projection pursuit, locally best invariant test