Open Access
2012 An asymptotically Gaussian bound on the Rademacher tails
Iosif Pinelis
Author Affiliations +
Electron. J. Probab. 17: 1-22 (2012). DOI: 10.1214/EJP.v17-2026


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.


Download Citation

Iosif Pinelis. "An asymptotically Gaussian bound on the Rademacher tails." Electron. J. Probab. 17 1 - 22, 2012.


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

zbMATH: 1252.60023
MathSciNet: MR2924368
Digital Object Identifier: 10.1214/EJP.v17-2026

Primary: 60E15
Secondary: 60F10 , 60G50 , 62G10 , 62G15 , 62G35

Keywords: Esscher--Cram\'er tilt transform , Generalized moments , large deviations , Probability inequalities , Rade\-macher random variables , self-normalized sums , Student's test , Sums of independent random variables , Tchebycheff--Markov systems

Vol.17 • 2012
Back to Top