Grand Lebesgue norm estimation for binary random variables, with applications
Probability
2015-07-29 v1
Abstract
We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates.
Cite
@article{arxiv.1507.07576,
title = {Grand Lebesgue norm estimation for binary random variables, with applications},
author = {Eugene Ostrovsky and Leonid Sirota},
journal= {arXiv preprint arXiv:1507.07576},
year = {2015}
}