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In search of an optimal kernel for a bias correction method for density estimators

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  • Sakhanenko, Lyudmila

Abstract

We consider a bias correction method for kernel density estimators based on a generalized jack-knifing with different bandwidths. We compare it with a standard kernel density estimation method with fourth order kernels, since both methods have the same rate of convergence. The bias corrected method has a tuning parameter. We investigate how to optimize the constant in the asymptotical mean integrated squared error of the bias corrected estimator with respect to the tuning parameter. We also explore whether an optimal kernel exists. This paper answers on the questions posed in section 3.2 of Jones and Foster (1993) where only numerical investigation was given.

Suggested Citation

  • Sakhanenko, Lyudmila, 2017. "In search of an optimal kernel for a bias correction method for density estimators," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 42-50.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:42-50
    DOI: 10.1016/j.spl.2016.10.028
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    References listed on IDEAS

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    1. Choongrak Kim & Sungsoo Kim & Mira Park & Hakbae Lee, 2006. "A bias reducing technique in kernel distribution function estimation," Computational Statistics, Springer, vol. 21(3), pages 589-601, December.
    2. Sakhanenko, Lyudmila, 2015. "Rate acceleration for estimators of integral curves from diffusion tensor imaging (DTI) data," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 286-295.
    3. Kairat Mynbaev & Carlos Martins-Filho, 2010. "Bias reduction in kernel density estimation via Lipschitz condition," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 219-235.
    4. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1031-1057, December.
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