A1703
Title: Gaussian and bootstrap approximations for functional principal component regression
Authors: Hyemin Yeon - Kent State University (United States) [presenting]
Abstract: Asymptotic inference using functional principal component regression (FPCR) has long been considered difficult, largely because, upon any scalar scaling, the FPCR estimator fails to satisfy a central limit theorem, leading to the prevailing belief that it is unsuitable for direct statistical inference. A new result establishes that, upon suitable operator scaling, valid Gaussian and bootstrap approximations hold for the FPCR estimator. This finding is applied to hypothesis testing for the significance of the slope function in functional regression models, demonstrating strong numerical performance of the resulting tests. The results yield powerful inferential tools for functional regression and pave the way for new lines of inferential methodology in more complex functional regression settings.
