Assessing and Visualizing Matrix Variate Normality

TL;DR

This paper introduces a comprehensive framework combining visual and statistical methods to assess the normality of three-way matrix data, enhancing analysis accuracy.

Contribution

It develops a novel visual method and a goodness of fit test based on Mahalanobis distance for evaluating matrix variate normality.

Findings

The MSD-based DD plot effectively visualizes normality.

The Kolmogorov-Smirnov test is robust across various data settings.

The framework performs well in simulation studies.

Abstract

A framework for assessing the matrix variate normality of three-way data is developed. The framework comprises a visual method and a goodness of fit test based on the Mahalanobis squared distance (MSD). The MSD of multivariate and matrix variate normal estimators, respectively, are used as an assessment tool for matrix variate normality. Specifically, these are used in the form of a distance-distance (DD) plot as a graphical method for visualizing matrix variate normality. In addition, we employ the popular Kolmogorov-Smirnov goodness of fit test in the context of assessing matrix variate normality for three-way data. Finally, an appropriate simulation study spanning a large range of dimensions and data sizes shows that for various settings, the test proves itself highly robust.