IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/280.html
   My bibliography  Save this paper

An inequality for uniform deviations of sample averages from their means

Author

Listed:

Abstract

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Using the new inequality we obtain tight bounds for empirical loss minimization learning.

Suggested Citation

  • Peter Bartlett & Gábor Lugosi, 1998. "An inequality for uniform deviations of sample averages from their means," Economics Working Papers 280, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:280
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/280.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Devroye, Luc, 1982. "Bounds for the uniform deviation of empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 72-79, March.
    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. Pal, Soumik, 2007. "Computing strategies for achieving acceptability: A Monte Carlo approach," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1587-1605, November.
    2. Lugosi, Gábor, 1995. "Improved upper bounds for probabilities of uniform deviations," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 71-77, October.
    3. Levon Demirdjian & Majid Mojirsheibani, 2019. "Kernel classification with missing data and the choice of smoothing parameters," Statistical Papers, Springer, vol. 60(5), pages 1487-1513, October.
    4. Xu, Jianjun & Tan, Xianming & Zhang, Runchu, 2010. "A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"," Journal of Econometrics, Elsevier, vol. 154(1), pages 35-41, January.
    5. Luc Devroye & Gábor Lugosi & Frederic Udina, 1998. "Inequalities for a new data-based method for selecting nonparametric density estimates," Economics Working Papers 281, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Ryan Cumings-Menon, 2022. "Differentially Private Estimation via Statistical Depth," Papers 2207.12602, arXiv.org.

    More about this item

    Keywords

    Vapnik-Chervonenkis inequality; uniform laws of large numbers; empirical risk; minimization;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:upf:upfgen:280. 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: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    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.