Joint Testing and False Discovery Rate Control in High-Dimensional Multivariate Regression
Yin Xia, Tony Cai, and Hongzhe Li
Multivariate regression with high-dimensional covariates has many applications in genomic and genetic research, in which some covariates are expected to be associated with multiple responses. This paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control. The test statistic is based on inverse regression and bias-corrected group lasso estimates of the regression coefficients and is shown to have a asymptotic chi-square null distribution. A row-wise multiple testing procedure is developed to identify the covariates associated with the responses. The procedure is shown to control the false discovery proportion and false discovery rate at a pre-specified level asymptotically. Simulations demonstrate the gain in power in detecting the covariates associated with the responses as compared to entry-wise testing. The test is applied to an ovarian cancer data set in order to identify the miRNA regulators that regulate protein expression.