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Nonparametric Kernel Density Estimation Near the Boundary

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  • Peter Malec
  • Melanie Schienle

Abstract

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the chosen kernel. We therefore suggest a refined version of the gamma kernel with an additional tuning parameter according to the shape of the density close to the boundary. We also provide a data-driven method for the appropriate choice of the modified gamma kernel estimator. In an extensive simulation study we compare the performance of this refined estimator to standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. We find that the finite sample performance of the proposed new estimator is superior in all settings. Two empirical applications based on high-frequency stock trading volumes and realized volatility forecasts demonstrate the usefulness of the proposed methodology in practice.

Suggested Citation

  • Peter Malec & Melanie Schienle, 2012. "Nonparametric Kernel Density Estimation Near the Boundary," SFB 649 Discussion Papers SFB649DP2012-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2012-047
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    3. Ma, Xiaobo & Karimpour, Abolfazl & Wu, Yao-Jan, 2020. "Statistical evaluation of data requirement for ramp metering performance assessment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 141(C), pages 248-261.
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    5. D.P. Amali Dassanayake & Igor Volobouev & A. Alexandre Trindade, 2017. "Local orthogonal polynomial expansion for density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 806-830, October.
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    7. 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.
    8. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
    9. Mohammadi, Faezeh & Izadi, Muhyiddin & Lai, Chin-Diew, 2016. "On testing whether burn-in is required under the long-run average cost," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 217-224.
    10. Jenny Farmer & Donald Jacobs, 2018. "High throughput nonparametric probability density estimation," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-29, May.

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    More about this item

    Keywords

    Kernel density estimation; boundary correction; asymmetric kernel;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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