Robust reduced-rank modeling via rank regression

•Proposed a rank-based estimation approach for reduced-rank regression.•Established asymptotic normality and efficiency of the estimator.•Investigated finite sample performance of the estimator.

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.