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Nonparametric estimation of a regression function with dependent observations

Author

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  • Wu, J. S.
  • Chu, C. K.

Abstract

This paper investigates performance of nonparametric kernel regression and its associated bandwidth selection for dependent observations. For short range dependent observations, it is shown that the convergence rate of asymptotic normality and the strong uniform convergence rate (SUCR) of the kernel estimator are of the same orders as those given for the case of independent observations. Also, Mallows' criterion is adjusted to correct for the effect of dependence on bandwidth selection. The bandwidth produced by modified Mallows' criterion is analyzed by a central limit theorem. The convergence rate of the bandwidth is of the same order as that given for the case of independent observations. On the other hand, for long range dependent observations, the SUCR of the kernel estimator could be slower or faster than that given for the case of independent observations, depending on the dependence structure.

Suggested Citation

  • Wu, J. S. & Chu, C. K., 1994. "Nonparametric estimation of a regression function with dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 149-160, March.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:1:p:149-160
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    Citations

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    Cited by:

    1. Sangyeol Lee & Okyoung Na & Seongryong Na, 2003. "On the cusum of squares test for variance change in nonstationary and nonparametric time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 467-485, September.
    2. 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.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    4. Liebscher, Eckhard, 1999. "Asymptotic normality of nonparametric estimators under [alpha]-mixing condition," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 243-250, July.
    5. Igor S. Borisov & Yuliana Yu. Linke & Pavel S. Ruzankin, 2021. "Universal weighted kernel-type estimators for some class of regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 141-166, February.

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