IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v32y2005i4p551-562.html
   My bibliography  Save this article

A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data

Author

Listed:
  • JAN W. H. SWANEPOEL
  • FRANCOIS C. VAN GRAAN

Abstract

. A new kernel distribution function (df) estimator based on a non‐parametric transformation of the data is proposed. It is shown that the asymptotic bias and mean squared error of the estimator are considerably smaller than that of the standard kernel df estimator. For the practical implementation of the new estimator a data‐based choice of the bandwidth is proposed. Two possible areas of application are the non‐parametric smoothed bootstrap and survival analysis. In the latter case new estimators for the survival function and the mean residual life function are derived.

Suggested Citation

  • Jan W. H. Swanepoel & Francois C. Van Graan, 2005. "A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 551-562, December.
  • Handle: RePEc:bla:scjsta:v:32:y:2005:i:4:p:551-562
    DOI: 10.1111/j.1467-9469.2005.00472.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2005.00472.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-9469.2005.00472.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. Catalina Bolancé & Montserrat Guillen, 2021. "Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk," Risks, MDPI, vol. 9(4), pages 1-23, April.
    2. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    3. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    4. Chacón, José E. & Monfort, Pablo & Tenreiro, Carlos, 2014. "Fourier methods for smooth distribution function estimation," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 223-230.
    5. Steven Abrams & Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2020. "Nonparametric estimation of the cross ratio function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 771-801, June.
    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. 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.
    8. David Mason & Jan Swanepoel, 2011. "A general result on the uniform in bandwidth consistency of kernel-type function estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 72-94, May.
    9. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    10. Suparna Biswas & Rituparna Sen, 2019. "Kernel Based Estimation of Spectral Risk Measures," Papers 1903.03304, arXiv.org, revised Dec 2023.
    11. D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.

    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:scjsta:v:32:y:2005:i:4:p:551-562. 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=0303-6898 .

    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.