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. 
Tests for multivariate normality based on canonical correlations
TLDR
New affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution, are proposed, which are found to offer higher power against many of the alternatives.
Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$-statistics
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of
Testing normality in any dimension by Fourier methods in a multivariate Stein equation
We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the
Multivariate Normality Tests Based on Principal Components
In this paper, we investigate some measures as tests of multivariate normality based on principal components. The idea was proposed by Srivastava and Hui(1987). They generalized Shapiro-Wilk
Testing for normality in any dimension based on a partial differential equation involving the moment generating function
We use a system of first-order partial differential equations that characterize the moment generating function of the d-variate standard normal distribution to construct a class of affine invariant
A new affine invariant test for multivariate normality based on beta probability plots
A new technique for assessing multivariate normality (MVN) is proposed in this work based on a beta transform of the multivariate normal data set. The statistic is the sum of interpoint squared
The Limit Distribution of an Invariant Test Statistic for Multivariate Normality
Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all
Joint Normality Test Via Two-Dimensional Projection
Extensive literature exists on how to test for normality, especially for identically and independently distributed (i.i.d) processes. The case of dependent samples has also been addressed, but only
A characterization of normality via convex likelihood ratios
The Use of Isotones for Comparing Tests of Normality Against Skew Normal Distributions
The problem of testing for multivariate normality has received much attention. Among the myriad of tests available, we confine ourselves to three affine invariant and simple to implement tests. In
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 97 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
Critical values and powers for tests of uniformity of directions under multivariate normality
The Rayleigh, Ajne, Gine and two new tests of uniformity of directions are investigated as tests for multivariate normality when the population mean vector and covariance matrix are assumed to be
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
...
1
2
3
4
5
...