Variable selection for functional regression models via the L1 regularization

In regression analysis, L1 regularizations such as the lasso or the SCAD provide sparse solutions, which leads to variable selection. We consider the variable selection problem where variables are given as functional forms, using L1 regularization. In order to select functional variables each of which is controlled by multiple parameters, we treat parameters as grouped parameters and then apply the group SCAD. A crucial issue in the regularization method is the choice of regularization parameters. We derive a model selection criterion for evaluating the model estimated by the regularization method via the group SCAD penalty. Results of simulation and real data analysis show the effectiveness of the proposed modeling strategy.