Estimation and inference for functional linear regression models with partially varying regression coefficients

Abstract

In this paper, we present a class of functional linear regression models with varying coefficients of a functional response on one or multiple functional predictors and scalar predictors. In particular, the approach can accommodate densely or sparsely sampled functional responses as well as multiple scalar and functional predictors. It also allows for the combination of continuous or categorical covariates. Tensor product B‐spline basis is proposed for the estimation of the bivariate coefficient functions. We show that our estimators hold asymptotic consistency and normality. Several numerical examples demonstrate superior performance of the proposed methods against two existing approaches. The proposed method is also applied to a real data example.