Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach

Reduced rank regression is considered when the criterion function is possibly non-smooth, which includes the previously un-studied reduced rank quantile regression. The approach used is based on empirical likelihood with a rank constraint. Asymptotic properties of the maximum empirical likelihood estimator (MELE) are established using general results on over-parametrized models. Empirical likelihood leads to more efficient estimators than some existing estimators. Besides, in the framework of empirical likelihood, it is conceptually straightforward to test the rank of the unknown matrix. The proposed methods are illustrated by some simulation studies and real data analyses.