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.

中文翻译：

---

具有部分变化的回归系数的函数线性回归模型的估计和推断

在本文中，我们提出了一类功能线性回归模型，其中一个或多个功能预测变量和标量预测变量具有不同的功能响应系数。特别地，该方法可以适应密集或稀疏采样的功能响应以及多个标量和功能预测器。它还允许连续或分类协变量的组合。建议使用张量积B样条来估计双变量系数函数。我们证明了我们的估计量具有渐近一致性和正态性。几个数值示例证明了所提出的方法相对于两种现有方法的优越性能。所提出的方法也适用于实际数据示例。