Title: Nonlinear envelope model for nonparametric regression
Authors: Zhihua Su - University of Florida (United States) [presenting]
Abstract: An envelope model is introduced for parsimonious nonparametric multivariate regression, where the regression function is assumed to lie in a reproducing kernel Hilbert space. This model extends earlier works on envelope models from the linear to the nonlinear case. The conditional independence relations offered by the envelope structure allow us to effectively reduce the dimensions of both the predictor and response while performing the regression. Along with the estimation procedure, we also developed inference tools to construct confidence intervals, prediction intervals, and for conducting hypothesis test based on the asymptotic distribution of the envelope estimate. Simulation studies show that our model achieves substantial efficiency gains compared with standard nonparametric regression, principal component regression, and partial least squares. We applied our method to two data sets in chemometrics and breast cancer applications.