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

Abstract

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.

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Iosif Pinelis. "An asymptotically Gaussian bound on the Rademacher tails." Electron. J. Probab. 17 1 - 22, 2012. https://doi.org/10.1214/EJP.v17-2026

Information

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

Subjects:
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

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