Partially Linear Functional Additive Models for Multivariate Functional Data

• Activity Number: 570 - New Frontiers of Functional Data Analysis
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yehua Li* and Raymond Wong and Zhengyuan Zhu
• Companies: University of California, Riverside and Texas A&M University and Iowa State University
• Keywords: Additive model; functional data; model selection; splines; principal components; prediction

Abstract

Motivated by a crop yield prediction application, we investigate a class of partially linear functional additive models that predicts a scalar response by both parametric effects of a multivariate predictor and nonparametric effects of a multivariate functional predictor. We jointly model multiple functional predictors that are cross-correlated using multivariate FPCA, and model the nonparametric effects of the principal component scores as additive components in the model. To address the high dimensional nature of functional data, we let the number of principal components diverge to infinity with the sample size, and adopt the COSSO penalty to select relevant components and regularize the fitting. A fundamental difference between our framework and the existing high dimensional additive models is that the principal component scores are estimated with error, and the magnitude of measurement error increases with the order of principal component. We establish the asymptotic convergence rate for our estimator. When the number of additive components is fixed, we also establish the asymptotic distribution for the partially linear coefficient.