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Bias reduction in kernel density estimation via Lipschitz condition

Author

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  • Kairat Mynbaev
  • Carlos Martins-Filho

Abstract

In this paper we propose a new nonparametric kernel-based estimator for a density function f which achieves bias reduction relative to the classical Rosenblatt–Parzen estimator. Contrary to some existing estimators that provide for bias reduction, our estimator has a full asymptotic characterisation including uniform consistency and asymptotic normality. In addition, we show that bias reduction can be achieved without the disadvantage of potential negativity of the estimated density – a deficiency that results from using higher order kernels. Our results are based on imposing global Lipschitz conditions on f and defining a novel corresponding kernel. A Monte Carlo study is provided to illustrate the estimator's finite sample performance.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:219-235
    DOI: 10.1080/10485250903266058
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    Cited by:

    1. Martins-Filho, Carlos & Ziegelmann, Flávio Augusto & Torrent, Hudson da Silva, 2013. "Local Exponential Frontier Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    2. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Canonical higher-order kernels for density derivative estimation," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1383-1387.
    3. Mynbaev, Kairat & Martins-Filho, Carlos, 2015. "Consistency and asymptotic normality for a nonparametric prediction under measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 166-188.
    4. Kairat Mynbaev & Carlos Martins-Filho, 2019. "Unified estimation of densities on bounded and unbounded domains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 853-887, August.
    5. Sakhanenko, Lyudmila, 2017. "In search of an optimal kernel for a bias correction method for density estimators," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 42-50.
    6. 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.
    7. Kairat Mynbaev & Carlos Martins-Filho & Aziza Aipenova, 2016. "A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 591-615, Emerald Group Publishing Limited.
    8. 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.

    More about this item

    JEL classification:

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

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