A Principal Components Based Moment Generating Function Test for Multivariate Normality

Madukaife, Mbanefo Solomon; Ossai, Everestus Okafor; Nduka, Uchenna Chinedu; Ugah, Tobias Ejiofor

doi:10.22034/jirss.2024.713812

A Principal Components Based Moment Generating Function Test for Multivariate Normality

Document Type : Original Article

Authors

Mbanefo Solomon Madukaife

Everestus Okafor Ossai

Uchenna Chinedu Nduka

Tobias Ejiofor Ugah

Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria

10.22034/jirss.2024.713812

Abstract

In this paper, we propose an alternative generalization of a recent test for univariate normality which is based on the empirical moment generating function to the multivariate case. We show, among other properties, that the proposed weighted L²-class of statistics is affine invariant and consistent. The empirical critical values of the proposed test are evaluated for different sample sizes, variable dimensions and values of the smoothing parameter through large scale simulations. The empirical power comparison of the test with a strong competitor shows that the test has a considerably high power performance, especially at large sample sizes as well as under heavy-tailed alternative distributions. The application of the statistic, together with its competitor, to six real-life datasets also supports the considerable good power performance of the proposed statistic as well as its ease of application.

Keywords

Empirical Critical Value

Moment Generating Function

Multivariate Normality

Principal Components

Weighted L2 -Statistic

Subjects

Computational Statistics

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