Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords
Abstract
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.
Keywords
Cite
@article{arxiv.1709.02166,
title = {Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords},
author = {Dominik Liebl and Stefan Rameseder and Christoph Rust},
journal= {arXiv preprint arXiv:1709.02166},
year = {2020}
}