S. Chobanyan, H. Salehi

On the Tail Estimation of the Norm of Rademacher Sums

The main aim of this paper is to prove a bilateral inequality for $P\big[\Vert \sum\limits_1^n a_kr_k \Vert > t\big] $, where $t>0$, $(a_k)$ are elements of a normed space, while $(r_k)$ are Rademacher functions. Then this inequality is applied for estimation of $ E\Vert \sum\limits_1^n a_kr_k \Vert $. As another corollary we give a maximal inequality for exchangeable random variables that has been published by A. R. Pruss in 1998.