Hypothesis testing for high-dimensional multivariate regression with false discovery rate control

Abstract

Motivated by applications in microarray data analysis, we consider the problem of estimating the row sparsity of the coefficient matrix in multivariate regression. The problem is formulated as a row-wise multiple testing problem. A new test statistic is constructed for each row of the coefficient matrix, and a row-wise multiple testing procedure is proposed. Our approach takes advantage of the row sparsity of the coefficient matrix to gain high power and handles the correlation structure of the error vector. Asymptotic distribution of the test statistic and asymptotic false discovery control of the row-wise multiple testing procedure are provided. Numerical results are also presented to evaluate the performance of the proposed method in both simulation studies and real data analysis.