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An adaptive estimation for covariate-adjusted nonparametric regression model

Author

Listed:
  • Feng Li

    (Zhengzhou University)

  • Lu Lin

    (Shandong University
    Qufu Normal University)

  • Yiqiang Lu

    (PLA Strategic Support Force Information Engineering University)

  • Sanying Feng

    (Zhengzhou University)

Abstract

For covariate-adjusted nonparametric regression model, an adaptive estimation method is proposed for estimating the nonparametric regression function. Compared with the procedures introduced in the existing literatures, the new method needs less strict conditions and is adaptive to covariate-adjusted nonparametric regression with asymmetric variables. More specifically, when the distributions of the variables are asymmetric, the new procedures can gain more efficient estimators and recover data more accurately by elaborately choosing proper weights; and for the symmetric case, the new estimators can obtain the same asymptotic properties as those obtained by the existing method via designing equal bandwidths and weights. Simulation studies are carried out to examine the performance of the new method in finite sample situations and the Boston Housing data is analyzed as an illustration.

Suggested Citation

  • Feng Li & Lu Lin & Yiqiang Lu & Sanying Feng, 2021. "An adaptive estimation for covariate-adjusted nonparametric regression model," Statistical Papers, Springer, vol. 62(1), pages 93-115, February.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01084-0
    DOI: 10.1007/s00362-019-01084-0
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Jun & Li, Gaorong & Feng, Zhenghui, 2015. "Checking the adequacy for a distortion errors-in-variables parametric regression model," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 52-64.
    3. 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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