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An inequality for uniform deviations of sample averages from their means

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  • Bartlett, Peter
  • Lugosi, Gábor

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, Theory of Pattern Recognition. Nauka, Moscow] and Pollard [1995, Uniform ratio limit theorems for empirical processes, Scand. J. Statist. 22, 271-278]. Using the new inequality we obtain tight bounds for empirical loss minimization learning.

Suggested Citation

  • Bartlett, Peter & Lugosi, Gábor, 1999. "An inequality for uniform deviations of sample averages from their means," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 55-62, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:1:p:55-62
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    References listed on IDEAS

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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;

    JEL classification:

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

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