Reduced rank regression with matrix projections for high-dimensional multivariate linear regression model

In this work, we incorporate matrix projections into the reduced rank regression method, and then develop reduced rank regression estimators based on random projection and orthogonal projection in high-dimensional multivariate linear regression model. We propose a consistent estimator of the rank of the coefficient matrix and achieve prediction performance bounds for the proposed estimators based on mean squared errors. Finally, some simulation studies and a real data analysis are carried out to demonstrate that the proposed methods possess good stability, prediction performance and rank consistency compared to some other existing methods.