Extremal properties of sums of Bernoulli random variables

Carlos A. León and François Perron

Statistics & Probability Letters, 2003, vol. 62, issue 4, 345-354

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.

Keywords: Large; deviations; Convex; ordering; Bernoulli; random; variables (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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