Robust reduced-rank modeling via rank regression

There are many applications in which several response variables are predicted with a common set of predictors. To take into account the possible correlations among the responses, estimators with restricted rank were introduced. However, existing methods for performing reduced-rank regression are often based on least squares procedure, which is adversely affected by outliers or heavy-tailed error distributions. In this work, we propose robust reduced-rank estimator via rank regression. As in univariate regression, the new method is much more efficient compared to its least-squares-based counterpart for many heavy-tailed distributions and is thus more robust. Asymptotic properties of the estimator are established and numerical studies are carried out to demonstrate its finite sample performance. (C) 2016 Elsevier B.V. All rights reserved.