Developments in Functional Regression Model for Network Structured Data

ABSTRACT In this paper, we propose a Network‐Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network‐structured settings. To assess predictive uncertainty, we develop a functional conformal prediction procedure that yields a distribution‐free prediction interval with guaranteed coverage. Through extensive evaluation on both simulated and real‐world datasets, we demonstrate that the explicit modeling of network structure yields substantive improvements in point‐prediction accuracy and markedly enhances the validity and precision of the resulting prediction intervals.