IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v37y1983i2p73-83.html
   My bibliography  Save this article

Relative efficiency and deficiency of kernel type estimators of smooth distribution functions

Author

Abstract

The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.

Suggested Citation

  • M. Falk, 1983. "Relative efficiency and deficiency of kernel type estimators of smooth distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 37(2), pages 73-83, June.
    • Handle: RePEc:bla:stanee:v:37:y:1983:i:2:p:73-83
    DOI: 10.1111/j.1467-9574.1983.tb00802.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9574.1983.tb00802.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9574.1983.tb00802.x?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
    ---><---

    Citations

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


    Cited by:

    1. Lemdani, Mohamed & Ould-Saïd, Elias, 2003. "-deficiency of the Kaplan-Meier estimator," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 145-155, June.
    2. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
    3. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    4. Shan Luo & Gengsheng Qin, 2017. "New non-parametric inferences for low-income proportions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 599-626, June.
    5. Falk, Michael & Reiss, Rolf-Dieter, 2003. "Efficient estimators and LAN in canonical bivariate POT models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 190-207, January.
    6. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    7. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 317-329, June.
    8. Arup Bose & Santanu Dutta, 2022. "Kernel based estimation of the distribution function for length biased data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 269-287, April.
    9. Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    10. Alevizos, Filippos & Bagkavos, Dimitrios & Ioannides, Dimitrios, 2019. "Efficient estimation of a distribution function based on censored data," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 359-364.
    11. Kouros Owzar & Pranab Kumar Sen, 2003. "Copulas: concepts and novel applications," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 323-353.
    12. Ralescu, Stefan S. & Puri, Madan L., 1996. "Weak convergence of sequences of first passage processes and applications," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 327-345, July.
    13. Mammitzsch Volker, 2007. "Optimal kernels," Statistics & Risk Modeling, De Gruyter, vol. 25(2), pages 153-172, April.
    14. 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.
    15. Cervellera, C. & Macciò, D., 2011. "A numerical method for minimum distance estimation problems," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 789-800, April.

    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:bla:stanee:v:37:y:1983:i:2:p:73-83. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.