We consider joint rank and variable selection in multivariate regression. Previously proposed joint rank and variable selection approaches assume that different responses are related to the same set of variables, which suggests using a group penalty on the rows of the coefficient matrix....

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the...