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Partial functional linear regression with autoregressive errors

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  • Piaoxuan Xiao
  • Guochang Wang

Abstract

In the presented paper, we introduce a partial functional linear model, where a scalar response variable is explained by a multivariate random variable and a functional random variable, and the relationship between the scalar response and both of the predictors is linear. Besides, the model has autoregressive errors. To estimate the model, we first expand the functional predictor and functional regression parametric on the functional principal component basis, and then estimate the coefficients for multivariate and functional regression parametric by a generalized least squares method. Theoretical properties are presented including the asymptotical normality for the multivariate coefficient and the optimal convergence rate for the functional regression parametric. Simulation studies are used to illustrate these characteristics. The proposed method is also applied on the power forecasting of photovoltaic systems data set.

Suggested Citation

  • Piaoxuan Xiao & Guochang Wang, 2022. "Partial functional linear regression with autoregressive errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(13), pages 4515-4536, June.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:13:p:4515-4536
    DOI: 10.1080/03610926.2020.1818097
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    Cited by:

    1. Asma Ben Saber & Abderrazek Karoui, 2024. "On some stable linear functional regression estimators based on random projections," Statistical Papers, Springer, vol. 65(7), pages 4147-4178, September.

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