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Activity Number: 422
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #309516
Title: Penalized Function-on-Function Regression
Author(s): Andrada Ivanescu*+ and Ana-Maria Staicu and Fabian Scheipl and Sonja Greven
Companies: East Carolina University and North Carolina State University and Ludwig-Maximilians-Universität München and Ludwig-Maximilians-Universität München
Keywords: functional data analysis ; functional regression model ; penalized splines ; multiple functional predictors ; tractography data
Abstract:

We propose a general framework for smooth regression of a functional response on one or multiple functional predictors. Using the mixed model representation of penalized regression expands the scope of function on function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed: 1) on the same or different domains than the functional response; 2) on a dense or sparse grid; and 3) with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a Diffusion Tensor Imaging (DTI) brain tractography dataset.


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