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Multiplicative bias correction for discrete kernels

Author

Listed:
  • Lynda Harfouche

    (University of Bejaia)

  • Smail Adjabi

    (University of Bejaia)

  • Nabil Zougab

    (University of Bejaia)

  • Benedikt Funke

    (Technical University of Dortmund)

Abstract

In this paper, we prove that two multiplicative bias correction techniques (MBC) can be applied for discrete kernels in the context of probability mass function estimation. First, some properties of the MBC discrete kernel estimators (bias, variance and mean integrated squared error) are investigated. Second, the popular cross-validation technique is adapted for bandwidth selection. Finally, a simulation study and a real data application for discrete data illustrate the performance of the MBC estimators based on dirac discrete uniform and triangular discrete kernels.

Suggested Citation

  • Lynda Harfouche & Smail Adjabi & Nabil Zougab & Benedikt Funke, 2018. "Multiplicative bias correction for discrete kernels," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 253-276, June.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:2:d:10.1007_s10260-017-0395-x
    DOI: 10.1007/s10260-017-0395-x
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    References listed on IDEAS

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    1. Chi-Yang Chu & Daniel J. Henderson & Christopher F. Parmeter, 2015. "Plug-in Bandwidth Selection for Kernel Density Estimation with Discrete Data," Econometrics, MDPI, vol. 3(2), pages 1-16, March.
    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. Funke, Benedikt & Kawka, Rafael, 2015. "Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 148-162.
    4. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    5. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    6. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
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    Cited by:

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    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
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