  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.
