Wilcoxon-type Multivariate Cluster Elastic Net

We propose a method for high dimensional multivariate regression that is robust to random error distributions that are heavy-tailed or contain outliers, while preserving estimation accuracy in normal random error distributions. We extend the Wilcoxon-type regression to a multivariate regression model as a tuning-free approach to robustness. Furthermore, the proposed method regularizes the L1 and L2 terms of the clustering based on k-means, which is extended from the multivariate cluster elastic net. The estimation of the regression coefficient and variable selection are produced simultaneously. Moreover, considering the relationship among the correlation of response variables through the clustering is expected to improve the estimation performance. Numerical simulation demonstrates that our proposed method overperformed the multivariate cluster method and other methods of multiple regression in the case of heavy-tailed error distribution and outliers. It also showed stability in normal error distribution. Finally, we confirm the efficacy of our proposed method using a data example for the gene associated with breast cancer.