IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i7-8p548-557.html
   My bibliography  Save this article

A note on the performance of the gamma kernel estimators at the boundary

Author

Listed:
  • Zhang, Shunpu

Abstract

The gamma kernel estimator is proposed in Chen [Chen, S.X., 2000. Probability density function estimation using gamma kernels. Annals of the Institute of Statistical Mathematics 52, 471-480] to estimate densities with support [0,[infinity]). It is shown in his paper that the gamma kernel estimator is non-negative, free of boundary bias, and achieves the optimal rate of convergence for the mean integrated squared error. Numerical results reported in Chen's paper show that, in the boundary region, the gamma kernel estimator even outperforms some widely used boundary corrected density estimators such as the boundary kernel estimator. However, our study finds that the gamma kernel estimator at x=0 is actually the reflection estimator when the double exponential kernel is used and is only boundary problem free when the estimated density has a shoulder at x=0 (i.e., the first derivative of the density at x=0 is zero). For densities not satisfying the shoulder condition, we show that the gamma kernel estimator has a severe boundary problem and its performance is inferior to that of the boundary kernel estimator.

Suggested Citation

  • Zhang, Shunpu, 2010. "A note on the performance of the gamma kernel estimators at the boundary," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 548-557, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:548-557
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00459-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    2. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    3. Shunpu Zhang & Rohana Karunamuni, 2010. "Boundary performance of the beta kernel estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 81-104.
    4. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Gery Geenens, 2021. "Mellin–Meijer kernel density estimation on $${{\mathbb {R}}}^+$$ R +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 953-977, October.
    3. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.
    4. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    5. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    6. Ouimet, Frédéric, 2022. "A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Weiran Lin & Qiuqin He, 2021. "The Influence of Potential Infection on the Relationship between Temperature and Confirmed Cases of COVID-19 in China," Sustainability, MDPI, vol. 13(15), pages 1-11, July.

    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. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    3. Masayuki Hirukawa & Irina Murtazashvili & Artem Prokhorov, 2022. "Uniform convergence rates for nonparametric estimators smoothed by the beta kernel," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1353-1382, September.
    4. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    5. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.
    6. Jiecheng Wang & Yantong Liu & Jincai Chang, 2022. "An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    7. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    8. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    9. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    10. Bouezmarni, T. & Mesfioui, M. & Rolin, J.M., 2007. "L1-rate of convergence of smoothed histogram," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1497-1504, August.
    11. Gery Geenens, 2014. "Probit Transformation for Kernel Density Estimation on the Unit Interval," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 346-358, March.
    12. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Nonparametric density estimation for multivariate bounded data," LIDAM Discussion Papers CORE 2007065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Bouezmarni, T. & Rombouts, J.V.K., 2009. "Semiparametric multivariate density estimation for positive data using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2040-2054, April.
    14. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    15. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    16. Shunpu Zhang & Rohana Karunamuni, 2010. "Boundary performance of the beta kernel estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 81-104.
    17. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    18. Chen, Rongda & Zhou, Hanxian & Jin, Chenglu & Zheng, Wei, 2019. "Modeling of recovery rate for a given default by non-parametric method," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    19. Funke, Benedikt & Kawka, Rafael, 2015. "Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 148-162.
    20. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.

    More about this item

    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:eee:stapro:v:80:y:2010:i:7-8:p:548-557. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.