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

TL;DR

This paper addresses instability in estimating functional linear regression models with points of impact, proposing a new sequential algorithm that improves accuracy, demonstrated through simulations and Google AdWords data.

Contribution

It introduces a novel sequential estimation algorithm that enhances the accuracy of parameter estimation in functional linear regression with points of impact.

Findings

The new algorithm significantly improves estimation stability and accuracy.

Simulation studies show better performance compared to existing methods.

Application to Google AdWords data demonstrates practical utility.

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.