Estimation of Low Rank High-Dimensional Multivariate Linear Models for Multi-Response Data

In this article, we study low rank high-dimensional multivariate linear models (LRMLM) for high-dimensional multi-response data. We propose an intuitively appealing estimation approach and develop an algorithm for implementation purposes. Asymptotic properties are established to justify the estimation procedure theoretically. Intensive simulation studies are also conducted to demonstrate performance when the sample size is finite, and a comparison is made with some popular methods from the literature. The results show the proposed estimator outperforms all of the alternative methods under various circumstances. Finally, using our suggested estimation procedure we apply the LRMLM to analyze an environmental dataset and predict concentrations of PM2.5 at the locations concerned. The results illustrate how the proposed method provides more accurate predictions than the alternative approaches.