Improving Estimation in Functional Linear Regression With Points of Impact: Insights Into Google AdWords. Issue 4 (1st October 2020)

• Record Type: Journal Article
• Authors: Liebl, Dominik; Rameseder, Stefan; Rust, Christoph
• Is Part Of: Journal of computational and graphical statistics. Volume 29:Issue 4(2020)
• Page Start: 814
• Page End: 826
• Publication Date: 2020-10-01
• Subjects: Functional data analysis -- Functional linear regression -- Online advertising -- Points of impact; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2020.1754224
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: The functional linear regression model with points of impact (PoI) is a recent augmentation of the classical functional linear model with many practically important applications. In this article, 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 PoI 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 materials .