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 procedure for estimating the parameters of this regression model can be very 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.

翻译：具有影响点的功能线性回归模型是具有许多实际重要应用的经典功能性线性模型最近得到的增强。然而,在这项工作中,我们证明估计这一回归模型参数的现有程序可能非常不准确。省略相关影响点的倾向是一个特别成问题的方面,造成可忽略的偏差。我们解释了这一问题的理论原因,并提出了新的顺序估算算法,从而大大改进了估算结果。我们的估算算法与使用深入模拟研究的现有估算程序进行了比较。使用Google AdWords的数据证明了其适用性,Google AdWords是当今最重要的在线广告平台。