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A bias corrected nonparametric regression estimator

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  • Yao, Weixin
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211003270
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 2 ()
    Pages: 274-282

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:274-282

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    Related research

    Keywords: Bias reduction; Local linear regression; Nonparametric regression; Nonlinear smoother;

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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.
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