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Reduced-rank Regression in Sparse Multivariate Varying-Coefficient Models with High-dimensional Covariates

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction methods in sparse multivariate regression models. Previous studies on joint variable and rank selection have focused on parametric models while here we consider the more challenging varying-coefficient models which make the investigation on nonlinear interactions of variables possible. Spline approximation, rank constraints and concave group penalties are utilized for model estimation. Asymptotic oracle properties of the estimators are presented. We also propose reduced-rank independent screening to deal with the situation when the dimension is so high that penalized estimation cannot be efficiently applied. In simulations, we show the advantages of simultaneously performing variable and rank selection. A real data set is analyzed to illustrate the good prediction performance when incorporating interactions between genetic variables and an index variable.