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The matrix-variate normal distribution is a popular model forhigh-dimensional transposable data because it decomposes the dependencestructure of the random matrix into the Kronecker product of two covariancematrices: one for each of the row and column variables. We develop tests forassessing the form of the row (column) covariance matrix in high-dimensionalsettings while treating the column (row) dependence structure as a nuisance.Our tests are robust to normality departures provided that the Kroneckerproduct dependence structure holds. In simulations, we observe that theproposed tests maintain the nominal level and are powerful against thealternative hypotheses tested. We illustrate the utility of our approach byexamining whether genes associated with a given signalling network showcorrelated patterns of expression in different tissues and by studyingcorrelation patterns within measurements of brain activity collected usingelectroencephalography.

Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure