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Higher-Order Asymptotic Properties of Kernel Density Estimator with Plug-In Bandwidth

Author

Listed:
  • Shunsuke Imai

    (Faculty of Economics, Kyoto University, JAPAN)

  • Yoshihiko Nishiyama

    (Institute of Economic Research, Kyoto University, JAPAN,)

Abstract

This study investigates the effect of bandwidth selection via plug-in method on the asymptotic structure of the nonparametric kernel density estimator. We find that the plug-in method has no effect on the asymptotic structure of the estimator up to the order of O{(nh0)−1/2} = O(n−L/(2L+1)) for a bandwidth h0 and any kernel order L. We also provide the valid Edgeworth expansion up to the order of O{(nh0)−1} and find that the plug-in method starts to have an effect from on the term whose convergence rate is O{(nh0)−1/2h0} = O(n−(L+1)/(2L+1)). In other words, we derive the exact convergence rate of the deviation between the distribution functions of the estimator with a deterministic bandwidth and with the plug-in bandwidth. Monte Carlo experiments are conducted to see whether our approximation improves previous results.

Suggested Citation

  • Shunsuke Imai & Yoshihiko Nishiyama, 2022. "Higher-Order Asymptotic Properties of Kernel Density Estimator with Plug-In Bandwidth," KIER Working Papers 1076, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:1076
    as

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    References listed on IDEAS

    as
    1. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    2. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
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    More about this item

    Keywords

    nonparametric statistics; kernel density estimator; plug-in bandwidth; Edgeworth expansion;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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