On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model

Abstract

We propose a functional linear model to predict a functional response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g. functional principal components, splines), and the coefficients of the basis functions are estimated via optimizing a penalization criterion. Then effect lags are determined by simultaneously searching on a prior designed grid mesh based on minimization of a proposed prediction error criterion. Mathematical properties of the estimated regression functions and predicted responses are studied. The performance of the method is evaluated by extensive simulations and a real data analysis application on chronic obstructive pulmonary disease (COPD).

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Item Type:	Article
Authors/Creators:	Liu, H. https://orcid.org/0000-0002-3442-1722 Aivaliotis, G. https://orcid.org/0000-0003-4018-4820 Kumar, V. Houwing-Duistermaat, J.
Copyright, Publisher and Additional Information:	© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords:	Functional data analysis; Effect lag functional linear model; Functional principal component analysis; COPD
Dates:	Published: April 2024 Published (online): 8 November 2023 Accepted: 15 September 2023
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds)
Funding Information:	Funder Grant number Alan Turing Institute Not Known Alan Turing Institute No ref given EPSRC (Engineering and Physical Sciences Research Council) EP/N013980/1
Depositing User:	Symplectic Publications
Date Deposited:	01 Dec 2023 14:09
Last Modified:	16 May 2024 15:45
Status:	Published
Publisher:	Springer
Identification Number:	10.1007/s12561-023-09393-7
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:206071

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On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model

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