Functional Additive Models

• Activity Number: 120
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Fang Yao*+ and Hans-Georg Mueller
• Companies: University of Toronto and University of California, Davis
• Keywords: Additive Model ; Functional Data Analysis ; Functional Regression ; Linear Model ; Principal Components ; Smoothing

Abstract

In commonly used functional regression models, the regression of a scalar/functional response on the functional predictor is assumed to be linear. We relax the linearity assumption and propose to replace it by an additive structure. This leads to a widely applicable and much more flexible framework for functional regression models. The proposed functional additive regression models are suitable for both scalar and functional responses. The utilization of functional principal components in an additive rather than linear way leads to substantial broadening of the scope of functional regression models and emerges as a natural approach, as the uncorrelatedness of the functional principal components is shown to lead to a straightforward implementation. The proposed approach is illustrated by an application to gene expression time course data.