A Normality Test for Multivariate Dependent Samples

TL;DR

This paper introduces a new normality test for multivariate dependent samples based on Mardia's kurtosis, providing a simple, computationally efficient method with good power properties demonstrated through simulations.

Contribution

It derives the asymptotic distribution of Mardia's kurtosis for dependent samples, enabling reliable normality testing in realistic, correlated data scenarios.

Findings

The test has good power in various dependence scenarios.

The derived distribution simplifies implementation and reduces computational load.

Simulation results validate the effectiveness of the proposed method.

Abstract

Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis, derive closed-form expressions of its asymptotic distribution for statistically dependent samples, under the null hypothesis of normality and a mixing condition. The calculus is long and tedious but the final result is simple and is implemented with a low computational burden. The proposed expression of the test power exhibits good properties on various scenarios; this is illustrated by computer experiments by means of copulas.