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A multiplicative bias reduction method for nonparametric regression

Author

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  • Linton, Oliver
  • Nielsen, Jens Perch

Abstract

We introduce a multiplicative bias reducing estimator (MBRE) for nonparametric regression. We show that our estimator has optimal pointwise convergence rate n4/9, when positive kernels are used. A simulation study comparing our procedure with the higher order kernel method is included.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:3:p:181-187
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    Citations

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    Cited by:

    1. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    2. Scholz, Michael & Nielsen, Jens Perch & Sperlich, Stefan, 2015. "Nonparametric prediction of stock returns based on yearly data: The long-term view," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 143-155.
    3. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    4. Wenzhuan Zhang & Yingcun Xia, 2012. "Twicing local linear kernel regression smoothers," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 399-417.
    5. Yao, Weixin, 2012. "A bias corrected nonparametric regression estimator," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 274-282.
    6. Jens Perch Nielsen & Carsten Tanggaard & M.C. Jones, 2007. "Local Linear Density Estimation for Filtered Survival Data, with Bias Correction," CREATES Research Papers 2007-13, Department of Economics and Business Economics, Aarhus University.
    7. Naito, Kanta & Yoshizaki, Masahiro, 2009. "Bandwidth selection for a data sharpening estimator in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1465-1486, August.
    8. Funke, Benedikt & Hirukawa, Masayuki, 2021. "Bias correction for local linear regression estimation using asymmetric kernels via the skewing method," Econometrics and Statistics, Elsevier, vol. 20(C), pages 109-130.
    9. Nielsen, Jens Perch & Tanggaard, Carsten & Jones, M. C., 2003. "Local Linear Density Estimation for Filtered Survival Data, with Bias Correction," Finance Working Papers 03-9, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    10. Perch Nielsen, Jens & Tanggaard, Carsten, 2000. "Boundary and Bias Correction in Kernel Hazard Estimation," Finance Working Papers 00-7, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    11. Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
    12. Bischofberger, Stephan M. & Hiabu, Munir & Mammen, Enno & Nielsen, Jens Perch, 2019. "A comparison of in-sample forecasting methods," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 133-154.

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