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Strong consistency of the internal estimator of nonparametric regression with dependent data

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  • Shen, Jia
  • Xie, Yuan

Abstract

In this paper, the strong consistency of the multivariate internal nonparametric estimator is investigated under strong mixing dependence assumption. This estimator is particularly easy to use when we model the regression function by additive nonparametric structure. The pointwise strong consistency and its rate are given as well as that over a compact set, under suitable conditions.

Suggested Citation

  • Shen, Jia & Xie, Yuan, 2013. "Strong consistency of the internal estimator of nonparametric regression with dependent data," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1915-1925.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1915-1925
    DOI: 10.1016/j.spl.2013.04.027
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    References listed on IDEAS

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    1. Oliver Linton & David Jacho-Chávez, 2010. "On internally corrected and symmetrized kernel estimators for nonparametric regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 166-186, May.
    2. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    3. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    4. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    5. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
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    Cited by:

    1. Huijun Guo & Youming Liu, 2017. "Strong consistency of wavelet estimators for errors-in-variables regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 121-144, February.
    2. Huijun Guo & Youming Liu, 2019. "Regression estimation under strong mixing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 553-576, June.
    3. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    4. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2024. "Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency," Mathematics, MDPI, vol. 12(12), pages 1-23, June.

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