Domain Selection for Functional Linear Models

Abstract

In this talk, I will discuss scalar-on-function linear regression, focusing on the domain selection problem. While the functional predictor X(t) is observed over a compact domain, the scalar response Y may be associated with X(t) only on a specific subdomain. Hall and Hooker (2016) proposed two methods for estimating this domain of association but highlighted the challenge of accurately identifying the domain boundary when the coefficient function transitions smoothly to zero. To address this issue, we adopt a reproducing kernel Hilbert space (RKHS) framework, introducing a domain estimator and establishing its asymptotic properties under mild smoothness conditions.
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