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讲座简介：
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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. We consider a more flexible varying-coefficient model which makes the investigation on nonlinear interactions and study of dynamic patterns possible for multivariate regression analysis. Spline approximation, rank constraints and concave group penalties are utilized for model estimation. Asymptotic oracle properties of the estimators are presented. We also propose a reduced-rank independence screening procedure to deal with the situation that the dimension of the covariates is so high that penalized estimation cannot be directly applied. Our proposed method is illustrated by simulation studies, and by an analysis of a real data example to identify genetic factors and evaluate their effects on multivariate responses under environmental influences. |
