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A0432
Title: Semiparametric functional regression models with multivariate functional predictors Authors:  Yehua Li - University of California at Riverside (United States) [presenting]
Abstract: Motivated by a crop yield prediction application using temperature trajectories and other scalar predictors, we consider two classes of semiparametric functional regression models. We jointly model cross-correlated functional predictors using multivariate functional principal component analysis (mFPCA), and use the mFPCA scores as predictors 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 theoretical properties for both models, letting the number of principal components diverge to infinity. A fundamental difference between our framework and the existing high-dimensional semiparametric regression models is that the mFPCA 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.