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

@article{Baringhaus1988ACT,
  title={A consistent test for multivariate normality based on the empirical characteristic function},
  author={Ludwig Baringhaus and Norbert Henze},
  journal={Metrika},
  year={1988},
  volume={35},
  pages={339-348}
}
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 for the composite hypothesisHd: the law ofX1 is a non-degenerate normal distribution, based on a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residualsSn−1/2(Xj − $$\bar X_n $$ ) and its pointwise limit exp (−1/2|t|2) underHd. The… 
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References

SHOWING 1-10 OF 12 REFERENCES
A test for normality based on the empirical characteristic function
SUMMARY An omnibus test of normality is proposed, which has high power against many alternative hypotheses. The test uses a weighted integral of the squared modulus of the difference between the
9 Tests of unvariate and multivariate normality
Publisher Summary This chapter discusses the tests of univariate and multivariate normality. The tests discussed in the chapter are tests based on descriptive measures, test based on cumulants, tests
On Assessing Multivariate Normality
SUMMARY We discuss procedures for assessing multivariate normality based on properties of radii and angles of the multivariate normal distribution, and suggest that different procedures may be
Recent and classical tests for normality - a comparative study
We give a critical synopsis of classical and recent tests for univariate normality, our emphasis being on procedures which are consistent against all alternatives. The power performance of some
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 the Effect of Substituting Parameter Estimators in Limiting $\chi^2 U$ and $V$ Statistics
On decrit les effets des estimateurs auxilliaires sur la distribution limite de la statistique Tn(λ) pour les cas ou Tn(λ) est une statistique U ou V avec une distribution limite de type χ 2
Consistency of some tests for multivariate normality
SummaryWe prove that the tests of Csörgő (1986) and of Baringhaus and Henze (1988) for multivariate normality, both based on the empirical characteristic function, are consistent.
Testing for Normality in Arbitrary Dimension
On etend le theoreme de convergence faible univariable de Murota et Takeuchi (1981) pour la transformee de Mahalanobis de la fonction caracteristique empirique a d variables, d≥1
Testing multivariate normality
SUMMARY Previous work on testing multivariate normality is reviewed. Coordinate-dependent and invariant procedures are distinguished. The arguments for concentrating on tests of linearity of
Methods for statistical data analysis of multivariate observations
  • R. Gnanadesikan
  • Mathematics, Computer Science
    A Wiley publication in applied statistics
  • 1977
TLDR
Reduction of Dimensionality, Assessment of Specific Aspects of Multivariate Statistical Models, and Summarization and Exposure.
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