Visual assessment of matrix-variate normality

In recent years, the analysis of three-way data has become ever more prevalent in the literature. It is becoming increasingly common to analyse such data by means of matrix-variate distributions, the most prevalent of which is the matrix-variate normal distribution. Although many methods exist for assessing multivariate normality, there is a relative paucity of approaches for assessing matrix-variate normality. Herein, a new visual method is proposed for assessing matrix-variate normality by means of a distance-distance plot. In addition, a testing procedure is discussed to be used in tandem with the proposed visual method. The proposed approach is illustrated via simulated data as well as an application on analysing handwritten digits.