Nonconvex penalized reduced rank regression and its oracle properties in high dimensions

Sparse reduced rank regression achieves dimension reduction and variable selection simultaneously. In this paper, for a class of nonconvex penalties, we give sufficient conditions that guarantee the oracle estimator is a local minimizer and stronger conditions that guarantee it is a global minimizer, with probability tending to one in an ultra-high dimensional setting. We carry out simulations to investigate the performance of the estimator. A real data set is analyzed for illustration.