Abstract
In this paper, we first transform a multivariate normal random vector into a random vector with elements that are approximately independent standard normal random variables. Then we propose the multivariate version generalized from the univariate normality test based on kurtosis from the literature. Power is investigated through the Monte Carlo Simulation with different significance level, dimension, and sample size. To assess the validity and accuracy of the new tests, we carry a comparative study with several other existing tests by selecting certain types of symmetric and asymmetric alternative distributions.
Highlights
Testing multivariate normality is a key premise in modern statistical inference
We propose some multivariate tests that are an extension of univariate tests proposed by Bonett and Seier (2002) based on transformation proposed by Anscombe and Glynn (1983)
A simulation was performed to compute the power of the proposed new test statistics denoted by Dw∗, Dw∗∗ and Dβ∗, Dβ∗∗ respectively according to different measure of kurtosis
Summary
Testing multivariate normality is a key premise in modern statistical inference. Kim (2016) recently proposed a robustified Jarque-Bera test for multivariate and univariate normality. He investigates the multivariate versions of the Jarque-Bera test and its modifications using orthogonalization or an empirical standardization of data. Alva and Estrada (2009) has proposed a goodness-of-fit test for multivariate normality which is based on Shapiro-Wilk’s statistics, one of the best omnibus tests for the univariate normality. Hanusz and Tarasinska (2014) proposed two new tests for multivariate normality based on
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