Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords

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 R-package FunRegPoI and additional R-codes are provided in the online supplementary material.

带影响点的函数线性回归模型（Functional Linear Regression Model with Points of Impact）是经典函数线性模型的新兴拓展，具备诸多极具实际价值的应用场景。然而，本研究表明，当前用于估计该回归模型参数的数据驱动方法存在严重的不稳定性与精度缺陷。尤为突出的问题是，该方法易遗漏关键影响点，进而引发遗漏变量偏差。本研究阐明了该问题的理论根源，并提出一种全新的序贯估计算法，可显著提升估计效果。本研究通过深度仿真实验，将所提序贯估计算法与现有估计方法进行了对比验证。本研究借助当前全球最重要的在线广告平台谷歌广告（Google AdWords）的真实数据，验证了所提方法的适用性。在线补充材料中提供了FunRegPoI R包及额外的R代码脚本。