Dr. Yehua Li

Title: Semiparametric Functional Regression Models with Multivariate Functional Predictors

Abstract:

Motivated by an application on predicting crop yield using temperature trajectories and other scalar predictors, we consider two classes of semiparametric functional regression models, both of which are extensions of the classic functional linear models. We jointly model multiple functional predictors that are cross-correlated using multivariate functional principal component analysis (mFPCA), and use the mFPCA score as extracted features in a second stage semiparametric regression. In the proposed partially linear functional additive models (PLFAM), we predict the scalar response by both the parametric effects of the multivariate predictor and additive nonparametric effects of the mFPCA scores, and adopt the component selection and smoothing operator (COSSO) penalty to select relevant components and regularize the fitting. In the second class of semiparametric functional regression models, we also consider the interactions between the functional and multivariate predictors, where we assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor to avoid the curse of dimensionality. We establish theoretic properties for both models, where we let the number of principal components diverge to infinity with the sample size. A fundamental difference between our framework and the existing high-dimensional semiparametric regression models is that the principal component scores are estimated with errors, the magnitudes of which increase with the order of FPC. The practical performances of the proposed methods are illustrated through analysis of the motivating crop yield data.