Abstract The functional linear regression model with points of impact (PoI) is a recent augmentation of the classical functional linear model with many practically important applications. In this article, however, we demonstrate that the existing data-driven procedure for estimating the parameters of this regression model can be very instable and inaccurate. The tendency to omit relevant PoI is a particularly problematic aspect resulting in omitted-variable biases. We explain the theoretical reason for this problem and propose a new sequential estimation algorithm that leads to significantly improved estimation results. Our estimation algorithm is compared with the existing estimation procedure using an in-depth simulation study. The applicability is demonstrated using data from Google AdWords, today’s most important platform for online advertisements. The R-package FunRegPoI and additional R-codes are provided in the online supplementary materials.

中文翻译：

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通过影响点改进函数线性回归的估计：深入了解 Google AdWords

摘要 具有影响点 (PoI) 的函数线性回归模型是经典函数线性模型的最新扩展，具有许多实际重要的应用。然而，在本文中，我们证明了用于估计此回归模型参数的现有数据驱动程序可能非常不稳定和不准确。遗漏相关 PoI 的倾向是一个特别有问题的方面，导致遗漏变量偏差。我们解释了这个问题的理论原因，并提出了一种新的顺序估计算法，可以显着改善估计结果。我们的估计算法使用深入的模拟研究与现有的估计程序进行了比较。使用来自 Google AdWords 的数据证明了适用性，当今最重要的在线广告平台。在线补充材料中提供了 R 包 FunRegPoI 和其他 R 代码。