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About the rate function in concentration inequalities for suprema of bounded empirical processes

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  • Marchina, Antoine

Abstract

We provide new deviation inequalities in the large deviations bandwidth for suprema of empirical processes indexed by classes of uniformly bounded functions associated with independent and identically distributed random variables. The improvements we get concern the rate function which is, as expected, the Legendre transform of the suprema of the log-Laplace transform of the pushforward measure by the functions of the considered class (up to an additional corrective term). Our approach is based on a decomposition in martingale together with some comparison inequalities.

Suggested Citation

  • Marchina, Antoine, 2019. "About the rate function in concentration inequalities for suprema of bounded empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3967-3980.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3967-3980
    DOI: 10.1016/j.spa.2018.11.010
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    References listed on IDEAS

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    1. Iosif Pinelis, 2014. "An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality," Risks, MDPI, vol. 2(3), pages 1-44, September.
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