An asymptotically Gaussian bound on the Rademacher tails

Details An asymptotically Gaussian bound on the Rademacher tails An asymptotically Gaussian bound on the Rademacher tails

2010-07-13

arxiv.org/abs/1007.2137v3

Mathematics

Probability

The discussion and references are expanded; the proofs of Lemmas 2.2 and 2.3 are simplified

Scientific paper

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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