In this paper, we study the partially functional linear regression model in which there are both functional predictors and traditional multivariate predictors. The existing approach is based on approximation using functional principal component analysis which has some limitations. We propose an alternative framework based on reproducing kernel Hilbert spaces (RKHS) which has not been investigated in the literature for the partially functional case. Asymptotic normality of the non-functional part is also shown. Even when reduced to the purely functional linear regression, our results extend the existing results in two aspects: rates are established using both prediction risk and RKHS norm, and faster rates are possible if greater smoothness is assumed. Some simulations are used to demonstrate the performance of the proposed estimator.

中文翻译：

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再现核希尔伯特空间中的部分函数线性回归

在本文中，我们研究了部分函数线性回归模型，其中既有函数预测变量，也有传统多元预测变量。现有方法基于使用函数主成分分析的近似，这具有一些局限性。我们提出了一种基于再现内核希尔伯特空间（RKHS）的替代框架，该框架在文献中尚未针对部分功能情况进行研究。还显示了非功能部分的渐近正态性。即使简化为纯函数线性回归，我们的结果在两个方面扩展了现有结果：使用预测风险和 RKHS 范数建立利率，如果假设更大的平滑度，则可能会更快。一些模拟用于证明所提出的估计器的性能。