Sparse Reduced-Rank Regression with Covariance Estimation
Multivariate linear regression is a technique that attempts to infer linear relationships between response variables and a set of input variables. The standard multivariate regression model assumes observations from different subjects are uncorrelated and the least squares estimates of the regression parameters can be obtained through separate univariate regressions.
There are many extensions to this model that seek to address this naive solution. There are two main approaches through which we can improve on this model. The first is to reduce the number of parameters in the model through variable selection. The second approach attempts to exploit the correlations between the response variables.
Reduced-rank regression assumes a low rank structure on the coefficient matrix and provides a nice framework. Chen and Huang propose a new model that fits under the reduced-rank regression framework, but also employs variable selection and estimation of the correlation among error terms.