Let $X_1, X_2,\ldots$ be independent, mean zero, uniformly bounded random variables with $S_n = X_1 + \cdots + X_n$. Optimal criteria are determined on the length and location of an interval $\Gamma$ so that $P(S_n \in \Gamma)$ is proportional to $(|\Gamma|/\sqrt{\operatorname{Var} S_n)} \wedge 1$. The proof makes an unusual use of support considerations.
Publié le : 1995-01-14
Classification:
Berry-Esseen theorem,
interval concentration of partial sums,
local limit theorems,
probabilities of small intervals,
probability approximations via support considerations,
60G50,
60E15,
60F99
@article{1176988394,
author = {Hahn, Marjorie G. and Klass, Michael J.},
title = {Uniform Local Probability Approximations: Improvements on Berry-Esseen},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 446-463},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988394}
}
Hahn, Marjorie G.; Klass, Michael J. Uniform Local Probability Approximations: Improvements on Berry-Esseen. Ann. Probab., Tome 23 (1995) no. 3, pp. 446-463. http://gdmltest.u-ga.fr/item/1176988394/