Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.

中文翻译：

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再现核希尔伯特空间中的结构化功能加性回归。

功能可加模型 (FAM) 为涉及功能预测变量的回归提供了灵活而简单的框架。在加法而非线性结构中使用数据驱动基础自然扩展了经典的函数线性模型。然而，选择非线性加性组件的关键问题研究较少。在这项工作中，我们提出了一种新的正则化框架，用于在再生核希尔伯特空间的背景下进行结构估计。所提出的方法利用了功能主成分，这极大地促进了实现和理论分析。选择和估计是通过使用惩罚的惩罚最小二乘法实现的，该惩罚鼓励加性组件的稀疏结构。研究了收敛速度等理论特性。通过模拟研究和实际数据应用证明了经验性能。