Confidence intervals for high-dimensional multi-task regression

Regression problems among multiple responses and predictors have been widely employed in many applications, such as biomedical sciences and economics. In this paper, we focus on statistical inference for the unknown coefficient matrix in high-dimensional multi-task learning problems. The new statistic is constructed in a row-wise manner based on a two-step projection technique, which improves the inference efficiency by removing the impacts of important signals. Based on the established asymptotic normality for the proposed two-step projection estimator (TPE), we generate corresponding confidence intervals for all components of the unknown coefficient matrix. The performance of the proposed method is presented through simulation studies and a real data analysis.