A new Bayesian semiparametric test for multivariate normality that places a Dirichlet process prior on marginals, uses a Gaussian copula for dependence, and combines relative belief ratios with energy distance.
Testing for normality in any dimension based on a partial differential equation involving the moment generating function
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abstract
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 tests for normality in any dimension. We derive the limit null distribution of the resulting test statistics, and we prove consistency of the tests against general alternatives. In the case $d > 1$, a certain limit of these tests is connected with two measures of multivariate skewness. The new tests show strong power performance when compared to well-known competitors, especially against heavy-tailed distributions, and they are illustrated by means of a real data set.
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stat.ME 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Test
A new Bayesian semiparametric test for multivariate normality that places a Dirichlet process prior on marginals, uses a Gaussian copula for dependence, and combines relative belief ratios with energy distance.