A0365
Title: Estimation and model selection for nonparametric function-on-function regression
Authors: Yuedong Wang - University of California - Santa Barbara (United States) [presenting]
Abstract: Regression models with functional response and functional covariates have recently received significant attention. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. A unified framework is presented for estimation and model selection in nonparametric function-on-function regression. A general nonparametric functional regression model is considered, with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some existing models when selected components in the SS ANOVA decomposition are eliminated. New estimation procedures under either L1 or L2 penalty are proposed, and combining the SS ANOVA decomposition and the L1 penalty is shown to provide powerful tools for model selection and diagnostics. Consistency and convergence rates are established for estimates of the regression function and each component in its decomposition under both the L1 and L2 penalties. Simulation studies and real examples show that the proposed methods perform well.
