Grand Lebesgue norm estimation for binary random variables, with applications

2015/07/27 by Ostrovsky, Eugene, Sirota, Leonid
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1507.07576

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.

Related

• Bilateral tail estimate for distribution of self normalizes sums of independent centered random variables under natural norming
• Exact value for subgaussian norm of centered indicator random variable
• Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics
• Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition
• A counterexample for equivalence result between tails behavior and Grand Lebesgue Spaces norms