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Improving bias in kernel density estimation


  • Mynbaev, Kairat T.
  • Nadarajah, Saralees
  • Withers, Christopher S.
  • Aipenova, Aziza S.


For order q kernel density estimators we show that the constant bq in bias=bqhq+o(hq) can be made arbitrarily small, while keeping the variance bounded. A data-based selection of bq is presented and Monte Carlo simulations illustrate the advantages of the method.

Suggested Citation

  • Mynbaev, Kairat T. & Nadarajah, Saralees & Withers, Christopher S. & Aipenova, Aziza S., 2014. "Improving bias in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 106-112.
  • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:106-112
    DOI: 10.1016/j.spl.2014.07.014

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    References listed on IDEAS

    1. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    2. Kairat Mynbaev & Carlos Martins-Filho, 2010. "Bias reduction in kernel density estimation via Lipschitz condition," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 219-235.
    3. Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 357-379, April.
    4. Fan, Jianqing & Hu, Tien-Chung, 1992. "Bias correction and higher order kernel functions," Statistics & Probability Letters, Elsevier, vol. 13(3), pages 235-243, February.
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    Cited by:

    1. Mynbaev, Kairat & Martins-Filho, Carlos, 2017. "Reducing bias in nonparametric density estimation via bandwidth dependent kernels: L1 view," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 17-22.

    More about this item


    Density estimation; Bias; Higher order kernel;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General


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