Covariance‐based low‐dimensional registration for function‐on‐function regression. Issue 1 (5th August 2021)

• Record Type: Journal Article
• Authors: Boschi, Tobia; Chiaromonte, Francesca; Secchi, Piercesare; Li, Bing
• Is Part Of: Stat. Volume 10:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-08-05
• Subjects: functional data -- regression -- smoothing; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.404
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : We propose a new low‐dimensional registration procedure that exploits the relationship between the response and the predictor in a function‐on‐function regression. In this context, functional covariance components (FCCs) provide a flexible and powerful tool to represent the data in a low‐dimensional space, capturing the most meaningful modes of dependency between the two set of curves. Based on this reduced representation, our procedure aligns simultaneously the two sets of curves, in a way that optimizes the subsequent regression analysis. To implement our procedure, we use both the continuous registration (CR) algorithm and a novel parallel algorithm coded in R . We then compare it to other common registration approaches via simulations and an application to the AneuRisk data.