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Extremal properties of sums of Bernoulli random variables

Author

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  • León, Carlos A.
  • Perron, François

Abstract

We build optimal exponential bounds for the probabilities of large deviations of sums Sn=[summation operator]1n Xi of independent Bernoulli random variables from their mean n[mu]. These bounds depend only on the sample size n. Our results improve previous results obtained by Hoeffding and, more recently, by Talagrand. We also prove a global stochastic order dominance for the Binomial law and shows how this gives a new explanation of Hoeffding's results.

Suggested Citation

  • León, Carlos A. & Perron, François, 2003. "Extremal properties of sums of Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 345-354, May.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:345-354
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    Cited by:

    1. Antonov, Sergei N. & Kruglov, Victor M., 2010. "Sharpened versions of a Kolmogorov's inequality," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 155-160, February.
    2. Greene, Evan & Wellner, Jon A., 2016. "Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3701-3715.

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