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Matrix-covariate is now frequently encountered in many biomedical researches.It is common to fit conventional statistical models by vectorizingmatrix-covariate. This strategy, however, results in a large number ofparameters, while the available sample size is relatively too small to havereliable analysis results. To overcome the problem of high-dimensionality inhypothesis testing, variance component test has been proposed with promisedetection power, but is not straightforward to provide estimates of effectsize. In this work, we overcome the problem of high-dimensionality by utilizingthe inherent structure of the matrix-covariate. The advantage is thatestimation and hypothesis testing can be conducted simultaneously as in theconventional case, while the estimation efficiency and detection power can belargely improved, due to a parsimonious parameterization for the coefficientsof matrix-covariate. Our method is applied to test the significance ofgene-gene interactions in the PSQI data, and is applied to test ifelectroencephalography is associated with the alcoholic status in the EEG data,wherein sparse effects and low-rank effects of matrix-covariates areidentified, respectively.

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