Functional Generalized Model

• Activity Number: 144
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yichi Zhang*+ and Ana-Maria Staicu and Arnab Maity
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Functional Principal Component Analysis ; Nonparametric Regression ; Generalized Linear Model ; Additive Model

Abstract

We introduce a functional generalized model for semi-parametric modeling of the relation between a scalar response and functional covariates and discuss the estimation procedure. The methodology uses functional principal components analysis, which gives a parsimonious representation of the functional predictors as a linear combination of orthogonal eigenbasis functions and functional principal component scores, as well as greatly facilitates the estimation implementation. Our modeling approach assumes flexible non-parametric dependence between the response and the functional principal component scores, and allows for non-normal response. This modeling framework naturally extends the functional additive model, which restricts the dependence to an additive structure of non-linear functions of the scores. The proposed method is illustrated through simulations and real data application.