Dimension Reduction Methods for Functional Data
University of California, Davis
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.