Electronic Journal of Probability

An asymptotically Gaussian bound on the Rademacher tails

Iosif Pinelis

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An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal distribution, thus affirming a longstanding conjecture by Efron. Applications to sums of general centered uniformly bounded independent random variables and to the Student test are presented.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 35, 22 pp.

Accepted: 15 May 2012
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60F10: Large deviations 62G10: Hypothesis testing 62G15: Tolerance and confidence regions 60G50: Sums of independent random variables; random walks 62G35: Robustness

probability inequalities large deviations Rade\-macher random variables sums of independent random variables Student's test self-normalized sums Esscher--Cram\'er tilt transform generalized moments Tchebycheff--Markov systems

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Pinelis, Iosif. An asymptotically Gaussian bound on the Rademacher tails. Electron. J. Probab. 17 (2012), paper no. 35, 22 pp. doi:10.1214/EJP.v17-2026. https://projecteuclid.org/euclid.ejp/1465062357

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