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Quadratic regression for functional response models

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  • Matsui, Hidetoshi

Abstract

A problem of constructing a regression model with a functional predictor and a functional response is considered. A functional quadratic model is an extension of a functional linear model and includes the quadratic term that takes the interaction between two different time points of the functional data into consideration. Predictor and the coefficient functions in the model are supposed to be expressed by basis expansions, and then parameters included in the model are estimated by the penalized likelihood method assuming that the error function follows a Gaussian process. Monte Carlo simulations are conducted to illustrate the efficacy of the proposed method. Finally, the proposed method is applied to the analysis of meteorological data and the results are explored.

Suggested Citation

  • Matsui, Hidetoshi, 2020. "Quadratic regression for functional response models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 125-136.
    • Handle: RePEc:eee:ecosta:v:13:y:2020:i:c:p:125-136
    DOI: 10.1016/j.ecosta.2018.12.003
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    References listed on IDEAS

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    1. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
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    Cited by:

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    2. Ufuk Beyaztas & Han Lin Shang, 2021. "A partial least squares approach for function-on-function interaction regression," Computational Statistics, Springer, vol. 36(2), pages 911-939, June.
    3. Ufuk Beyaztas & Han Lin Shang & Aylin Alin, 2022. "Function-on-Function Partial Quantile Regression," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 149-174, March.

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