IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/1076.html
   My bibliography  Save this paper

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

    Download full text from publisher

    File URL: https://www.kier.kyoto-u.ac.jp/wp/wp-content/uploads/2022/03/DP1076.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    2. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    3. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    4. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    5. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    6. Yingcun Xia & Wolfgang Härdle & Oliver Linton, 2009. "Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator," SFB 649 Discussion Papers SFB649DP2009-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    8. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    9. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
    10. Vexler, Albert & Gao, Xinyu & Zhou, Jiaojiao, 2023. "How to implement signed-rank wilcox.test() type procedures when a center of symmetry is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    11. José E. Chacón & Carlos Tenreiro, 2012. "Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 523-548, September.
    12. Mokkadem, Abdelkader & Pelletier, Mariane, 2020. "Online estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 166(C).
    13. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series 438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 531-537.
    15. Hall, Peter & Wolff, Rodney C. L., 1995. "Estimators of integrals of powers of density derivatives," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 105-110, August.
    16. Giraitis, L. & Robinson, P.M., 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," LSE Research Online Documents on Economics 291, London School of Economics and Political Science, LSE Library.
    17. Støve, Bård & Tjøstheim, Dag, 2007. "A Convolution Estimator for the Density of Nonlinear Regression Observations," Discussion Papers 2007/25, Norwegian School of Economics, Department of Business and Management Science.
    18. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.
    19. Rudolf Grübel, 1994. "Estimation of density functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 67-75, March.
    20. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2012. "Estimating Derivatives in Nonseparable Models With Limited Dependent Variables," Econometrica, Econometric Society, vol. 80(4), pages 1701-1719, July.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kyo:wpaper:1076. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Makoto Watanabe (email available below). General contact details of provider: https://edirc.repec.org/data/iekyojp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.