An asymptotically Gaussian bound on the Rademacher tails
Probability
2017-01-17 v3 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1007.2137,
title = {An asymptotically Gaussian bound on the Rademacher tails},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1007.2137},
year = {2017}
}
Comments
The discussion and references are expanded; the proofs of Lemmas 2.2 and 2.3 are simplified