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Nonparametric kernel density estimation near the boundary

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  • Malec, Peter
  • Schienle, Melanie

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. It is shown that, in such settings, alternatives of asymmetric gamma kernel estimators are superior, but also differ in asymptotic and finite sample performance conditionally on the shape of the density near zero and the exact form of the chosen kernel. Therefore, a refined version of the gamma kernel with an additional tuning parameter adjusted according to the shape of the density close to the boundary is suggested. A data-driven method for the appropriate choice of the modified gamma kernel estimator is also provided. An extensive simulation study compares the performance of this refined estimator to those of standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. It is found 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

  • Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
  • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:57-76
    DOI: 10.1016/j.csda.2013.10.023
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    Cited by:

    1. Kokonendji, Célestin C. & Varron, Davit, 2016. "Performance of discrete associated kernel estimators through the total variation distance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 225-235.
    2. Masayuki Hirukawa & Mari Sakudo, 2015. "Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 41-63, March.
    3. repec:eee:insuma:v:74:y:2017:i:c:p:78-83 is not listed on IDEAS
    4. repec:taf:gnstxx:v:29:y:2017:i:4:p:806-830 is not listed on IDEAS
    5. Berry, Tyrus & Sauer, Timothy, 2017. "Density estimation on manifolds with boundary," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 1-17.
    6. repec:spr:aistmt:v:71:y:2019:i:4:d:10.1007_s10463-018-0663-z is not listed on IDEAS
    7. 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.
    8. 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.

    More about this item

    Keywords

    Kernel density estimation; Boundary correction; Asymmetric kernel;

    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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