Estimation and Model Selection Procedures in Generalized Functional Partially Additive Hybrid Model with Diverging Number of Covariates

We study generalized functional partially additive hybrid model (GF-PAHM) where the explanatory variables involve both infinite dimensional predictor processes viewed as functional data with measurement errors, and high-dimensional scalar covariates whose impact on the response is nonlinear.Despite extensive work focusing on functional linear models, little effort has been devoted to estimate coefficients and selecting the important additive components for the GFPAHM, which is complicated by the infinite-dimensional functional predictor.We investigate a nonconvex penalized likelihood estimator for simultaneous variable selection and estimation.The proposed method and theoretical development are quite challenging since the numbers of nonlinear components increase as the sample size increases.Asymptotic properties of the proposed shrinkage estimators are investigated.Extensive Monte Carlo simulations have been conducted and show that the proposed Statistica Sinica: Newly accepted Paper procedure works effectively even with moderate sample sizes, and analyze the biscuit dough data set as an illustration.