Index Models with Sparse Functional Data

• Activity Number: 439
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Gareth James*+ and Xinghao Qiao and Peter Radchenko
• Companies: University of Southern California and University of Southern California and University of Southern California
• Keywords: Functional Regression ; Index Models ; Mixed Effects Models ; Sparse Functional Data

Abstract

In a Functional Data Analysis (FDA) setting the regression problem involving one or more functional predictors has recently received a great deal of attention. Since functional predictors are infinite dimensional, performing a functional regression requires some form of dimension reduction. Most approaches use an unsupervised method, such as functional principal components analysis, to represent the predictors and then regress Y against the lower dimensional representation of X(t).

We propose a new approach which uses a multiple index model formulation to perform a supervised dimension reduction. In particular, our method uses a mixed effects model to handle sparsely observed functional predictors. We illustrate our method on both simulated and real world data and show that it can produce superior results relative to unsupervised approaches.