High-Dimensional Inference of Multivariate Linear Model

Music City Center 

We aim to estimate and conduct inference for the effects of multiple covariates of interest simultaneously, after adjusting for the effects of high-dimensional control variables under a multivariate linear model setting. A chi-square statistic is proposed, based on the residuals obtained from fitting the response variables and the target covariates to the control covariates via regularized estimation. Procedures for hypothesis testing and confidence interval construction are developed. The proposed procedures mitigate the potential overfitting errors from regularized estimation on the inference of the target parameters and account for the inherent interconnectivity between response variables.

High dimensional Inference

Multivariate

Hotelling-Lawley trace 

Section on Statistical Computing