The Annals of Probability

Mean absolute deviations of sample means and minimally concentrated binomials

Lutz Mattner

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This is a contribution to the theory of sums of independent random variables at the level of optimal explicit inequalities: we compute the optimal constants in Hornich's lower bounds for the mean absolute deviations of sample means. This is done by reducing the original problem to the elementary one of determining the minimally concentrated binomial distributions $B_{n,p}$ with fixed sample size parameter $n$.

Article information

Ann. Probab., Volume 31, Number 2 (2003), 914-925.

First available in Project Euclid: 24 March 2003

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 62G05: Estimation 60G50: Sums of independent random variables; random walks

Binomial distribution concentration function Hornich moment inequality sums of independent random variables


Mattner, Lutz. Mean absolute deviations of sample means and minimally concentrated binomials. Ann. Probab. 31 (2003), no. 2, 914--925. doi:10.1214/aop/1048516540.

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