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Bias reduction in kernel density estimation via Lipschitz condition

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  • Mynbaev, Kairat
  • Martins-Filho, Carlos

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 characterization 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

  • Mynbaev, Kairat & Martins-Filho, Carlos, 2009. "Bias reduction in kernel density estimation via Lipschitz condition," MPRA Paper 24904, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:24904
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    References listed on IDEAS

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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, December.
    2. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    3. 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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    Citations

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    Cited by:

    1. Kairat Mynbaev & Carlos Martins-Filho & Aziza Aipenova, 2016. "A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions," Advances in Econometrics, in: Gloria GonzÁlez-Rivera & R. Carter Hill & Tae-Hwy Lee (ed.),Essays in Honor of Aman Ullah, volume 36, pages 591-615, Emerald Publishing Ltd.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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    More about this item

    Keywords

    bias reduction; kernel density estimation; Lipschitz conditions;

    JEL classification:

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

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