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A bias corrected nonparametric regression estimator

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  • Yao, Weixin

Abstract

In this article, we propose a new method of bias reduction in nonparametric regression estimation. The proposed new estimator has asymptotic bias order h4, where h is a smoothing parameter, in contrast to the usual bias order h2 for the local linear regression. In addition, the proposed estimator has the same order of the asymptotic variance as the local linear regression. Our proposed method is closely related to the bias reduction method for kernel density estimation proposed by Chung and Lindsay (2011). However, our method is not a direct extension of their density estimate, but a totally new one based on the bias cancelation result of their proof.

Suggested Citation

  • Yao, Weixin, 2012. "A bias corrected nonparametric regression estimator," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 274-282.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:274-282
    DOI: 10.1016/j.spl.2011.10.006
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    References listed on IDEAS

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    1. Linton, Oliver & Nielsen, Jens Perch, 1994. "A multiplicative bias reduction method for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 181-187, February.
    2. Marco Di Marzio, 2004. "Boosting kernel density estimates: A bias reduction technique?," Biometrika, Biometrika Trust, vol. 91(1), pages 226-233, March.
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    Cited by:

    1. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    2. Xinyang Yu & Cheng Wang & Zhongqing Yang & Binyan Jiang, 2022. "Tuning selection for two-scale kernel density estimators," Computational Statistics, Springer, vol. 37(5), pages 2231-2247, November.

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