B0978
Title: Additive functional prediction models with multiple predictors
Authors: Byeong Park - Seoul National University (Korea, South) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Kyunghee Han - University of California, Davis (United States)
Abstract: We propose functional additive models for functional regression with a scalar response and multiple functional predictors that are additive in the functional principal components of the predictor processes. For the case of a single functional predictor, the functional principal components are uncorrelated, so that a simple application of a marginal regression technique can be applied when it is furthermore assumed that the predictor components are independent, as for example in the case of a single Gaussian predictor process. When one has multiple functional predictors this independence assumption cannot be justified and therefore the dependency of the predictor components needs to be addressed. This motivates us to propose a new smooth backfitting technique for the estimation of the additive component functions in functional additive models with multiple functional predictors. A major difficulty in developing this technique is that the eigenfunctions and therefore the functional principal components of the predictor processes, which are the arguments of the proposed additive model, are unknown and need to be estimated from the data. We investigate how this required estimation of the functional principal components affects the estimation of the additive component functions and develop a complete asymptotic theory. We also study the finite sample properties of the proposed method through a simulation study and a real data example.
