Jane-Ling Wang
University of California, Davis

Dimension Reduction Methods for Functional Data

Functional data are intrinsically infinite dimensional, so the analysis of them typically involves some dimension reduction tools, such as functional principle component analysis or a dimension reduction model that involves finitely many indices. In this talk, we will first review various dimension reduction approaches that have been adopted in the literature, and discuss whether they are applicable to dense or sparse functional data and how noise is handled in each case. Then, we will focus on several dimension reduction methods that involve either a single index or multiple indices in the functional regression setting. We present two approaches that can handle both densely and sparsely observed functional data when the observed data are possibly contaminated with noise. Theoretical as well as numerical results will be presented to demonstrate the performance of both approaches.