Abstract: Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy 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, a variance-component test has been proposed with superior detection power, but it 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. One advantage of our method 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. Another merit is that, unlike existing methods, the proposed method avoids the problem of choosing identifiability constraints for the model parameters. Our method is applied to test the significance of gene-gene interactions in the PSQI data, and to test the association between electroencephalography and the alcoholic status in the EEG data.

Key words and phrases: High-dimensionality, hypothesis testing, low-rank, matrix-covariate, tensor.