Variable selection in regression models including functional data predictors

The variable selection and parameter estimation problem is researched in the framework of mixed-type regression model with both functional and multivariate predictors, which broadens the scope of functional data analysis and the application fields of variable selection methodology. First the functional predictors are projected into spaces spanned by functional principal component basis functions. Then variable selection and parameter estimation are implemented simultaneously for the multivariate predictors and derived projection predictors in the form of grouping, where the tuning parameter of the penalized term is adaptively selected and the loss function is based on absolute median loss function. As to the optimization procedure, by introducing slack variables, it is transformed into a linear programming problem with several constraint conditions, which simplifies the computation. The simulation results illustrate that the proposed method performs quite well in variable selection and parameter estimation in the mixed-type regression model.