Reproducing Kernel Hilbert space approach to Functional Regression for general exponential families
Speaker: Carlos Valencia
Date: June 7, 2013
Time: 4:00 pm – 5:00 pm
Location: 122 Illini Hall (Conference Room)
Sponsor: Statistics Department
We study a smoothness regularization estimator for an infinite dimensional parameter in an exponential family model with functional predictors. We focus on the Reproducing Kernel Hilbert space approach and show that, regardless the generality of the method, minimax optimal convergence rates are achieved. This research project enhances the set of tools that can be used for Functional Data Analysis, specifically, allowing for a computational convenient estimation of the regression problem in settings where the response is discrete or the zero mean additive error assumption is not appropiate. In order to derive the asymptotic analysis of the estimator, we developed a simultaneous diagonalization tool for two positive definite operators: the kernel operator and the operator defined by the second Frechet derivative of the expected data fit functional. By using the proposed simultaneous diagonalization tool we obtained sharper bounds on the minimax rates.