The Annals of Probability

Mean absolute deviations of sample means and minimally concentrated binomials

Lutz Mattner

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Abstract

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

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

Dates
First available in Project Euclid: 24 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1048516540

Digital Object Identifier
doi:10.1214/aop/1048516540

Mathematical Reviews number (MathSciNet)
MR1964953

Zentralblatt MATH identifier
1021.60015

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

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

Citation

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. https://projecteuclid.org/euclid.aop/1048516540


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References

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