使用影响点改进函数线性回归中的估计：Google AdWords的见解
Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords
摘要：
带影响点的泛函线性回归模型是经典泛函线性模型的一个新的扩展，具有许多重要的实际应用。然而，在这项工作中，我们证明了现有的数据驱动的过程，估计这个回归模型的参数可能是非常不稳定和不准确的。忽略相关影响点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，并提出了一个新的序贯估计算法，导致显着改善的估计结果。我们的估计算法与现有的估计程序进行了比较，使用深入的模拟研究。适用性证明使用数据从谷歌AdWords，今天最重要的在线广告平台。在线补充材料中提供了\textsf{R} -包\texttt{FunRegPoI}和其他\textsf{R} -代码。
英文摘要：
The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications. In this work, 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 points of impact 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 \textsf{R}-package \texttt{FunRegPoI} and additional \textsf{R}-codes are provided in the online supplementary material.
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