A new approach to varying-coefficient additive models with longitudinal covariates

Abstract

The varying-coefficient additive model is a novel tool for analyzing functional data. The model generalizes both the varying-coefficient model and the additive model, and retains their merits as an effective dimension reduction model that is flexible yet easily interpretable. However, the original method only works for densely recorded functional response processes with time-invariant covariates. To broaden its applicability, the model is extended to allow for time-dependent covariates and a new fitting approach is proposed that can handle sparsely recorded functional response processes. Consistency and L2 rate of convergence are developed for the proposed estimators of the unknown functions. A simple algorithm is developed that overcomes the computational difficulty caused by the non-convexity of the objective function. The proposed approach is illustrated through a simulation study and a real data application.