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An inequality for uniform deviations of sample averages from their means

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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
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    1. Devroye, Luc, 1982. "Bounds for the uniform deviation of empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 72-79, March.
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    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

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