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

Haiyan Liu (), Georgios Aivaliotis, Vijay Kumar and Jeanine Houwing-Duistermaat
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Haiyan Liu: University of Leeds
Georgios Aivaliotis: University of Leeds
Vijay Kumar: University of Sussex
Jeanine Houwing-Duistermaat: University of Leeds

Statistics in Biosciences, 2024, vol. 16, issue 1, No 1, 24 pages

Abstract: 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).

Keywords: Functional data analysis; Effect lag functional linear model; Functional principal component analysis; COPD (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s12561-023-09393-7

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