IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v122y2017icp42-50.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216302279
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.10.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    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. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Canonical higher-order kernels for density derivative estimation," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1383-1387.
    2. SCHAFGANS, Marcia M.A. & ZINDE-WALSH, Victoria, 2007. "Robust Average Derivative Estimation," Cahiers de recherche 12-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Martins-Filho, Carlos & Ziegelmann, Flávio Augusto & Torrent, Hudson da Silva, 2013. "Local Exponential Frontier Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    4. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Normal reference bandwidths for the general order, multivariate kernel density derivative estimator," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2198-2205.
    5. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    6. repec:cep:stiecm:/2011/557 is not listed on IDEAS
    7. Ariane Hanebeck & Bernhard Klar, 2021. "Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1229-1247, December.
    8. Langrené, Nicolas & Warin, Xavier, 2021. "Fast multivariate empirical cumulative distribution function with connection to kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    9. John Stachurski & Vance Martin, 2008. "Computing the Distributions of Economic Models via Simulation," Econometrica, Econometric Society, vol. 76(2), pages 443-450, March.
    10. Kairat Mynbaev & Carlos Martins-Filho & Aziza Aipenova, 2016. "A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 591-615, Emerald Group Publishing Limited.
    11. Mynbaev, Kairat & Martins-Filho, Carlos, 2015. "Consistency and asymptotic normality for a nonparametric prediction under measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 166-188.
    12. Yulia Kotlyarova & Marcia M Schafgans & Victoria Zinde-Walsh, 2011. "Adapting Kernel Estimation to Uncertain Smoothness," STICERD - Econometrics Paper Series 557, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Wan, Yuanyuan & Xu, Haiqing, 2015. "Inference in semiparametric binary response models with interval data," Journal of Econometrics, Elsevier, vol. 184(2), pages 347-360.
    14. Marcia M Schafgans & Victoria Zinde-Walshyz, 2008. "Smoothness Adaptive AverageDerivative Estimation," STICERD - Econometrics Paper Series 529, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    15. Mynbaev, Kairat T. & Nadarajah, Saralees & Withers, Christopher S. & Aipenova, Aziza S., 2014. "Improving bias in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 106-112.
    16. Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 357-379, April.
    17. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    18. Hu, Qirui, 2024. "Change point analysis of functional variance function with stationary error," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    19. Kairat Mynbaev & Carlos Martins-Filho, 2019. "Unified estimation of densities on bounded and unbounded domains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 853-887, August.
    20. Ana Maria Herrera & Pinar Ozbay, 2005. "A Dynamic Model of Central Bank Intervention," Working Papers 0501, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    21. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

    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:122:y:2017:i:c:p:42-50. 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.