A0867
Title: Hypothesis testing for functional linear models via bootstrapping
Authors: Yinan Lin - Chongqing Normal University (China)
Zhenhua Lin - National University of Singapore (Singapore) [presenting]
Abstract: Hypothesis testing for the slope in functional linear regression is both practically and theoretically important. A novel test is introduced for the nullity of the slope function by recasting it as a high-dimensional vector testing problem via functional principal component analysis (FPCA). This transformation overcomes the ill-posedness inherent in functional regression and enhances numerical stability. The approach employs a bootstrap of the maximum statistic and capitalizes on the natural variance-decay in functional data, yielding higher empirical power in small samples or under weak signals. The tests' validity and consistency are proven when principal components are estimated from data, and it is shown that their asymptotic properties remain intact even if all empirical components are included. This stands in sharp contrast to slope estimation, where one must carefully choose most root-n components to ensure consistency. This highlights a key divergence between estimation and inference in this setting. To the best of knowledge, this is the first test to leverage all empirical FPCA components.
