Title: Domain selection for functional linear models: A dynamic RKHS approach
Authors: Jane-Ling Wang - University of California Davis (United States) [presenting]
Shu-Chin Lin - University of California Davis (United States)
Abstract: In conventional scalar-on-function linear regression model, the entire trajectory of the predictor process on the whole domain is used to model the response variable. However, the response may only be associated with the covariate process $X$ on a subdomain. We consider the problem of estimating the domain of association when assuming that the regression coefficient function is nonzero on a subinterval. This problem was first considered few years ago, and the difficulty in estimating the domain has been pointed out. We resolve this through a two-steps procedure to estimate the unknown components, where in the first step we estimate the domain based on the reproducing kernel Hilbert space (RKHS) approach and in the second step the regression function is estimated. We motivate the two-step procedure and show that it provides consistent estimator for the domain under mild smoothness assumptions. A simulation study illustrates the effectiveness of the proposed approach.