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Uniform consistency rate of kNN regression estimation for functional time series data

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  • Nengxiang Ling
  • Shuyu Meng
  • Philippe Vieu

Abstract

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.

Suggested Citation

  • Nengxiang Ling & Shuyu Meng & Philippe Vieu, 2019. "Uniform consistency rate of kNN regression estimation for functional time series data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(2), pages 451-468, April.
    • Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:451-468
    DOI: 10.1080/10485252.2019.1583338
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    Cited by:

    1. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    2. Wang, Ziqi & Liu, Changliang & Yan, Feng, 2022. "Condition monitoring of wind turbine based on incremental learning and multivariate state estimation technique," Renewable Energy, Elsevier, vol. 184(C), pages 343-360.
    3. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    4. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    5. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.

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