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 $n$.
Publié le : 2003-04-14
Classification:
Binomial distribution,
concentration function,
Hornich,
moment inequality,
sums of independent random variables,
60E15,
62G05,
60G50
@article{1048516540,
author = {Mattner, Lutz},
title = {Mean absolute deviations of sample means and minimally concentrated binomials},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 914-925},
language = {en},
url = {http://dml.mathdoc.fr/item/1048516540}
}
Mattner, Lutz. Mean absolute deviations of sample means and minimally concentrated binomials. Ann. Probab., Tome 31 (2003) no. 1, pp. 914-925. http://gdmltest.u-ga.fr/item/1048516540/