Invariant tests for multivariate normality: a critical review

@article{Henze2002InvariantTF,
  title={Invariant tests for multivariate normality: a critical review},
  author={Norbert Henze},
  journal={Statistical Papers},
  year={2002},
  volume={43},
  pages={467-506}
}
  • N. Henze
  • Published 1 October 2002
  • Mathematics
  • Statistical Papers
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. 

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References

SHOWING 1-10 OF 96 REFERENCES

A class of invariant consistent tests for multivariate normality

Let be independent identically distributed random vectors in Rd d ≥ 1 , with sample mean [Xbar] n and sample covariance matrix S n . We present a class of practicable afflne-invariant tests for the

A consistent test for multivariate normality based on the empirical characteristic function

AbstractLetX1,X2, …,Xn be independent identically distributed random vectors in IRd,d ⩾ 1, with sample mean $$\bar X_n $$ and sample covariance matrixSn. We present a practicable and consistent test

On Mardia’s kurtosis test for multivariate normality

Let be independent identically distributed random(d-vectors with mean μ and nonsingular covariance matrix ∑ such that . We show that Mardia’s measure of multivariate kurtosis satisfies with σ2

A class of invariant procedures for assessing multivariate normality

SUMMARY Distribution theory pertaining to a class of invariant procedures for assessing multivariate normality is described. A Cramer-von Mises type statistic belonging to this class is investigated

On Tests for Multivariate Normality

Abstract The univariate skewness and kurtosis statistics, and b 2, and The W statistic proposed by Shapiro and Wilk are generalized to test a hypothesis of multivariate normality by use of S.N. Roy's

Some new tests for multivariate normality

SummaryA family of statistics is presented that can be used for testing goodness of fit to a parametric family. These statistics include Mardia's measure of multivariate kurtosis and Moore and

The asymptotic behavior of a variant of multivariate kurtosis

Let be independent identically distributed random d-dimensional column vectors with arithmetic mean [Xbar] n and empirical covariance matrix S n. Apart from the celebrated kurtosis measure of Mardia,

Shortcomings of generalized affine invariant skewness measures

This paper studies the asymptotic behavior of a generalization of Mardia's affine invariant measure of (sample) multivariate skewness. If the underlying distribution is elliptically symmetric, the

A New Graphical Test for Multivariate Normality

SYNOPTIC ABSTRACTA new methodology for assessing distributional assumptions of multivariate data, with graphical applications, is presented. The underlying procedure is based on transforming the
...