IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i2p337-356.html
   My bibliography  Save this article

Some new almost sure results on the functional increments of the uniform empirical process

Author

Listed:
  • Varron, Davit

Abstract

Given an observation of the uniform empirical process [alpha]n, its functional increments [alpha]n(u+an[dot operator])-[alpha]n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n-->[infinity] and an[downwards arrow]0. Under mild conditions on an, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process.

Suggested Citation

  • Varron, Davit, 2011. "Some new almost sure results on the functional increments of the uniform empirical process," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 337-356, February.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:2:p:337-356
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00264-4
    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. Berthet, Philippe, 2005. "Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 493-537, March.
    2. Einmahl, J. H.J., 1992. "The almost sure behavior of the weighted empirical process and the LIL for the weighted tail empirical process," Other publications TiSEM 5520438c-0aea-424b-b2c4-2, Tilburg University, School of Economics and Management.
    3. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
    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. Varron, Davit, 2008. "Some asymptotic results on density estimators by wavelet projections," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2517-2521, October.
    2. Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    3. Dindar, Zacharie, 2003. "Some more results on increments of the partially observed empirical process," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 25-37, August.
    4. Berthet, Philippe, 2005. "Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 493-537, March.
    5. Einmahl, J.H.J. & Khmaladze, E.V., 2007. "Central Limit Theorems For Local Emprical Processes Near Boundaries of Sets," Discussion Paper 2007-66, Tilburg University, Center for Economic Research.
    6. Dindar, Zacharie, 2000. "Random fractals generated by oscillations of the uniform empirical process," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 285-291, November.
    7. Djamal Louani & Alain Lucas, 2003. "Fractal Dimensions for Some Increments of the Uniform Empirical Process," Journal of Theoretical Probability, Springer, vol. 16(1), pages 59-86, January.
    8. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    9. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
    10. Paul Deheuvels & Sarah Ouadah, 2013. "Uniform-in-Bandwidth Functional Limit Laws," Journal of Theoretical Probability, Springer, vol. 26(3), pages 697-721, September.
    11. Paul Deheuvels, 1998. "On the Approximation of Quantile Processes by Kiefer Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 997-1018, October.
    12. Uwe Einmahl & David M. Mason, 2000. "An Empirical Process Approach to the Uniform Consistency of Kernel-Type Function Estimators," Journal of Theoretical Probability, Springer, vol. 13(1), pages 1-37, January.
    13. Einmahl, J.H.J. & Deheuvels, P., 2000. "Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications," Other publications TiSEM ac9bbdc0-62f8-4b48-9a84-1, Tilburg University, School of Economics and Management.
    14. Philippe Berthet, 1997. "On the Rate of Clustering to the Strassen Set for Increments of the Uniform Empirical Process," Journal of Theoretical Probability, Springer, vol. 10(3), pages 557-579, July.

    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:spapps:v:121:y:2011:i:2:p:337-356. 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/505572/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.