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

Author

Listed:
  • Haiyan Liu

    (University of Leeds)

  • Georgios Aivaliotis

    (University of Leeds)

  • Vijay Kumar

    (University of Sussex)

  • Jeanine Houwing-Duistermaat

    (University of Leeds
    Radboud University Nijmegen)

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).

Suggested Citation

  • Haiyan Liu & Georgios Aivaliotis & Vijay Kumar & Jeanine Houwing-Duistermaat, 2024. "On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(1), pages 1-24, April.
    • Handle: RePEc:spr:stabio:v:16:y:2024:i:1:d:10.1007_s12561-023-09393-7
    DOI: 10.1007/s12561-023-09393-7
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