Component Selection and Estimation for Functional Additive Models

• Activity Number: 628
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Hao (Helen) Zhang*+ and Hongxiao Zhu and Fang Yao
• Companies: University of Arizona and Virginia Tech and University of Toronto
• Keywords: functional data analysis ; additive models ; variable selection ; sparsity ; reproducing kernel Hilbert space ; COSSO

Abstract

Functional additive model provides a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for joint component selection and estimation in the context of the Reproducing Kernel Hilbert Space. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties, such as the existence and the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.