Dimension Reduction for Sparse Functional Data

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Edwin Kam Fai Lei*+ and Fang Yao and Yichao Wu
• Companies: University of Toronto and University of Toronto and NC State University
• Keywords: functional regression ; efficient dimension reduction ; inverse regression ; sparse functional data

Abstract

We propose an effective means of achieving dimension reduction in the context of functional regression with a scalar response. As commonly encountered in practice, trajectories of a functional predictor are sparsely observed and contaminated with noise, which forces one to adopt the strategy of pooling data together from the entire sample for consistent estimation and inference. The goal here is to find the effective dimension reduction space from such sparse functional data that assist in the prediction of a scalar response. Compared to sliced inverse regression, the proposed method lends itself well to sparse designs because it avoids partitioning the data into multiple slices and thus ensures the maximum use of data. Theoretical properties of the proposed method are established. Practical performance compared to functional linear model and functional sliced inverse regression is demonstrated with simulated and real data examples.