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Smoothed bootstrapping kernel density estimation under higher order kernel

Author

Listed:
  • Kun Yi

    (Graduate Shool of Economics, Kyoto University)

  • Yoshihiko Nishiyama

    (Institue of Economic Research, Kyoto University)

Abstract

Smoothed bootstrap method is a useful method to approximates the bias of Kernel density estimation. However, it can only be applied when the kernel function is of second order. In this study, we propose a novel method to generalize the smoothed bootstrap method to higher order kernel for estimating the bias and construct bias corrected estimator based on it. Theoretical formulation and numerical simulation demonstrate that the proposed method achieve better performance compared to the traditional bias correction method.

Suggested Citation

  • Kun Yi & Yoshihiko Nishiyama, 2022. "Smoothed bootstrapping kernel density estimation under higher order kernel," KIER Working Papers 1081, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:1081
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    References listed on IDEAS

    as
    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Hall, P. & Murison, R. D., 1993. "Correcting the Negativity of High-Order Kernel Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 103-122, October.
    3. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    kernel density estimation; smoothed bootstrap; bias estimation; higher order kernel;
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