IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v15y1984i3p279-294.html
   My bibliography  Save this article

On the convergence rate of maximal deviation distribution for kernel regression estimates

Author

Listed:
  • Konakov, V. D.
  • Piterbarg, V. I.

Abstract

Let (X, Y), X [set membership, variant] Rp, Y [set membership, variant] R1 have the regression function r(x) = E(Y|X = x). We consider the kernel nonparametric estimate rn(x) of r(x) and obtain a sequence of distribution functions approximating the distribution of the maximal deviation with power rate. It is shown that the distribution of the maximal deviation tends to double exponent (which is a conventional form of such theorems) with logarithmic rate and this rate cannot be improved.

Suggested Citation

  • Konakov, V. D. & Piterbarg, V. I., 1984. "On the convergence rate of maximal deviation distribution for kernel regression estimates," Journal of Multivariate Analysis, Elsevier, vol. 15(3), pages 279-294, December.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:3:p:279-294
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(84)90053-8
    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.

    Citations

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


    Cited by:

    1. Sokbae Lee & Ryo Okui & Yoon†Jae Whang, 2017. "Doubly robust uniform confidence band for the conditional average treatment effect function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1207-1225, November.
    2. Néstor Aguilera & Liliana Forzani & Pedro Morin, 2011. "On uniform consistent estimators for convex regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 897-908.
    3. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximation of suprema of empirical processes," CeMMAP working papers 44/12, Institute for Fiscal Studies.
    4. Rob Euwals & Bertrand Melenberg & Arthur van Soest, 1998. "Testing the predictive value of subjective labour supply data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 567-585.
    5. Qiao, Wanli, 2021. "Extremes of locally stationary Gaussian and chi fields on manifolds," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 166-192.
    6. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    7. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    8. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    9. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.
    10. Mojirsheibani, Majid, 2012. "A weighted bootstrap approximation of the maximal deviation of kernel density estimates over general compact sets," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 230-241.
    11. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
    12. Katharina Proksch, 2016. "On confidence bands for multivariate nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 209-236, February.
    13. Mojirsheibani, Majid, 2021. "A note on the performance of bootstrap kernel density estimation with small re-sample sizes," Statistics & Probability Letters, Elsevier, vol. 178(C).

    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:jmvana:v:15:y:1984:i:3:p:279-294. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.