, Volume 35, Issue 1, pp 339-348

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

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Abstract

LetX 1,X 2, …,X n be independent identically distributed random vectors in IR d ,d ⩾ 1, with sample mean \(\bar X_n \) and sample covariance matrixS n. We present a practicable and consistent test for the composite hypothesisH d: the law ofX 1 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 residualsS n −1/2 (X j \(\bar X_n \) ) and its pointwise limit exp (−1/2|t|2) underH d. The limiting null distribution of the test statistic is obtained, and a table with critical values for various choices ofn andd based on extensive simulations is supplied.