A low-rank based estimation-testing procedure for matrix-covariate regression

Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy, however, results in a large number of parameters, while the available sample size is relatively too small to have reliable analysis results. To overcome the problem of high-dimensionality in hypothesis testing, variance component test has been proposed with promise detection power, but is not straightforward to provide estimates of effect size. In this work, we overcome the problem of high-dimensionality by utilizing the inherent structure of the matrix-covariate. The advantage is that estimation and hypothesis testing can be conducted simultaneously as in the conventional case, while the estimation efficiency and detection power can be largely improved, due to a parsimonious parameterization for the coefficients of matrix-covariate. Our method is applied to test the significance of gene-gene interactions in the PSQI data, and is applied to test if electroencephalography is associated with the alcoholic status in the EEG data, wherein sparse effects and low-rank effects of matrix-covariates are identified, respectively.