Variable bandwidth kernel regression estimation
ESAIM: Probability and Statistics, Tome 25 (2021), pp. 55-86

In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in ℝ2 to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O($$4) under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

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DOI : 10.1051/ps/2021003
Classification : 62G07, 62E20, 62H12
Keywords: Kernel regression estimation, variable bandwidth, bias reduction, central limit theorem 
@article{PS_2021__25_1_55_0,
     author = {Nakarmi, Janet and Sang, Hailin and Ge, Lin},
     title = {Variable bandwidth kernel regression estimation},
     journal = {ESAIM: Probability and Statistics},
     pages = {55--86},
     year = {2021},
     publisher = {EDP-Sciences},
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     mrnumber = {4224733},
     zbl = {1466.62286},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2021003/}
}
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Nakarmi, Janet; Sang, Hailin; Ge, Lin. Variable bandwidth kernel regression estimation. ESAIM: Probability and Statistics, Tome 25 (2021), pp. 55-86. doi: 10.1051/ps/2021003

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