Adaptive smoothing spline estimator for the function-on-function linear regression model

Fabio Centofanti (), Antonio Lepore, Alessandra Menafoglio, Biagio Palumbo and Simone Vantini
Additional contact information
Fabio Centofanti: University of Naples Federico II
Antonio Lepore: University of Naples Federico II
Alessandra Menafoglio: MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano
Biagio Palumbo: University of Naples Federico II
Simone Vantini: MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano

Computational Statistics, 2023, vol. 38, issue 1, No 10, 216 pages

Abstract: Abstract In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the R package adass, openly available online on CRAN.

Keywords: Functional data analysis; Function-on-function linear regression; Adaptive smoothing; Functional regression (search for similar items in EconPapers)
JEL-codes: C13 C19 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-022-01223-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01223-6

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-022-01223-6

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().