Covariance-based low-dimensional registration for function-on-function regression

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.

This is the peer reviewed version of the following article: Boschi, T., Chiaromonte, F., Secchi, P., & Li, B. (2021). "Covariance-based low-dimensional registration for function-on-function regression". Stat, 10, no. 1. e404., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.


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Work Title Covariance-based low-dimensional registration for function-on-function regression
Open Access
  1. Tobia Boschi
  2. Francesca Chiaromonte
  3. Piercesare Secchi
  4. Bing Li
  1. Function-on-function regression
  2. Functional data registration
  3. Covariance operator
License In Copyright (Rights Reserved)
Work Type Article
  1. Stat
Publication Date July 12, 2021
Publisher Identifier (DOI)
Deposited August 04, 2022




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Work History

Version 1

  • Created
  • Added FCC_stat_light.pdf
  • Added Creator Tobia Boschi
  • Added Creator Francesca Chiaromonte
  • Added Creator Piercesare Secchi
  • Added Creator Bing Li
  • Published
  • Updated Keyword Show Changes
    • Function-on-function regression, Functional data registration, Covariance operator
  • Updated