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Convergence rate of kernel regression estimation for time series data when both response and covariate are functional

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  • Nengxiang Ling

    (Hefei University of Technology)

  • Lingyu Wang

    (Hefei University of Technology)

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

We investigate kernel estimates in the functional nonparametric regression model when both the response and the explanatory variable (the covariate) are functional. The rates of almost complete and uniform almost complete convergence of the estimator are obtained under some mild $$\alpha $$α-mixing functional sample. Finally, a simulation study is carried out to illustrate the finite sample performance of the estimator.

Suggested Citation

  • Nengxiang Ling & Lingyu Wang & Philippe Vieu, 2020. "Convergence rate of kernel regression estimation for time series data when both response and covariate are functional," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 713-732, August.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:6:d:10.1007_s00184-019-00757-y
    DOI: 10.1007/s00184-019-00757-y
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    References listed on IDEAS

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    1. Lecoutre, Jean-Pierre, 1990. "Uniform consistency of a class of regression function estimators for Banach-space valued random variable," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 145-149, July.
    2. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    3. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    4. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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