Statistical Papers

, Volume 43, Issue 4, pp 467–506

Invariant tests for multivariate normality: a critical review

  • Norbert Henze
Survey article

DOI: 10.1007/s00362-002-0119-6

Cite this article as:
Henze, N. Statistical Papers (2002) 43: 467. doi:10.1007/s00362-002-0119-6


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 X1,...,Xn 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.

Keywords and Phrases

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 

AMS Subject Classifications

62G10 62F05 

Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  • Norbert Henze
    • 1
  1. 1.Institut für Mathematische StochastikUniversität KarlsruheKarlsruheGermany

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