Based on the multivariate mean-shift regression model, we propose a new
sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier
detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate
outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix
encourage the low-rank row sparse structure of coefficient matrix and help to achieve
dimension reduction and variable selection. An algorithm is developed for solving our
problem. In our simulation and real-data application, our new method shows competitive
performance compared to other methods.