The matrix-variate normal distribution is a popular model for high-dimensional transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices, one for each of the row and column variables. However, there is a lack of hypothesis testing procedures for the row or column covariance matrix in high-dimensional settings. Tests for assessing the sphericity, identity and diagonality hypothesis for the row (column) covariance matrix in high-dimensional settings while treating the column (row) dependence structure as a ‘nuisance’ parameter are introduced. The proposed tests are robust to normality departures provided that the Kronecker product dependence structure holds. In simulations, the proposed tests appear to maintain the nominal level and they tended to be powerful against the alternative hypotheses tested. The utility of the proposed tests is demonstrated by analyzing a microarray and an electroencephalogram study. The proposed testing methodology has been implemented in the R package HDTD.
- Covariance matrix
- high-dimensional settings
- hypothesis testing
- matrix-valued random variables
- transposable data
Touloumis, A., Marioni, J. C., & Tavaré, S. (Accepted/In press). Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure. Statistica Sinica. https://doi.org/10.5705/ss.202018.0268