An asymptotically Gaussian bound on the Rademacher tails

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.

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

References in corpus (3)

• Exact inequalities for sums of asymmetric random variables, with applications
• New estimates of the convergence rate in the Lyapunov theorem
• Tchebycheff systems and extremal problems for generalized moments: a brief survey