Estimation and variable selection for generalized functional partially varying coefficient hybrid models

In this article, we propose a novel class of generalized functional partially varying coefficient hybrid models and variable selection procedure in which the explanatory variables include infinite dimensional predictor processes, treated as functional data with measurement errors, and high-dimensional scalar covariates with a diverging number of parameters. We focus on estimating coefficients and selecting the important variables in the high-dimensional covariates, which is complicated by the infinite-dimensional functional predictor, and one of our contributions is to characterize the effects of regularization on the resulting estimators. The proposed method is based on B-spline basis and functional principal component basis function approximation and a class of variable selection procedures using nonconcave penalized likelihood. Under some regularity conditions, we establish the consistency and oracle properties of the resulting shrinkage estimator, and empirical illustrations are given by simulation and illustrate its application using the biscuit dough dataset.