An asymptotically Gaussian bound on the Rademacher tails

Document Type

Article

Publication Date

7-9-2012

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.

Publication Title

Electronic Journal of Probability

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