Grand Lebesgue norm estimation for binary random variables, with applications

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.

References in corpus (6)

• Exact inequalities for sums of asymmetric random variables, with applications
• Exact value for subgaussian norm of centered indicator random variable
• The Kearns--Saul inequality for Bernoulli and Poisson-binomial distributions
• Hoeffding's inequality for sums of weakly dependent random variables
• Moment and Tail Inequalities for Polynomial Martingales
• Subgaussian and strictly subgaussian random variable