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Bias reduction in kernel density estimation

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  • Yousri Slaoui

Abstract

In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, ‘The stochastic approximation method for the estimation of a multivariate probability density’, J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.

Suggested Citation

  • Yousri Slaoui, 2018. "Bias reduction in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 505-522, April.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:505-522
    DOI: 10.1080/10485252.2018.1442927
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    Cited by:

    1. Timothy Fortune & Hailin Sang, 2020. "Shannon Entropy Estimation for Linear Processes," JRFM, MDPI, vol. 13(9), pages 1-13, September.
    2. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    3. Slaoui Yousri, 2019. "Optimal bandwidth selection for recursive Gumbel kernel density estimators," Dependence Modeling, De Gruyter, vol. 7(1), pages 375-393, January.
    4. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.

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