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Function-on-function quadratic regression models

Author

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  • Sun, Yifan
  • Wang, Qihua

Abstract

A quadratic regression model where the covariate and the response are both functional is considered, which is a reasonable extension of common function-on-function linear regression models. Methods to estimate the coefficient functions, predict unknown response and test significance of the quadratic term are developed in functional principal component regression paradigm. Asymptotic theories for these approaches are also established. A simulation study is presented to demonstrate the finite sample performances of the proposed methods and an application to real data is used to illustrate the improvement that can be gained by comparing to the function-on-function linear models.

Suggested Citation

  • Sun, Yifan & Wang, Qihua, 2020. "Function-on-function quadratic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301616
    DOI: 10.1016/j.csda.2019.106814
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    Cited by:

    1. 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.
    2. 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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