We derive two-sided bounds on the rate of convergence of moments in the central limit theorem. A variety of norming constants is considered, and it is shown that a very delicate alteration to these constants can have a significant effect on the rate. Indeed, the influence of norming constants on rates of convergence of moments is of a more subtle nature than in the central limit theorem itself. We present several examples to illustrate some extreme cases.
Publié le : 1982-11-14
Classification:
Central limit theorem,
moments,
norming constants,
rates of convergence,
60F05,
60G50
@article{1176993721,
author = {Hall, Peter},
title = {Bounds on the Rate of Convergence of Moments in the Central Limit Theorem},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 1004-1018},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993721}
}
Hall, Peter. Bounds on the Rate of Convergence of Moments in the Central Limit Theorem. Ann. Probab., Tome 10 (1982) no. 4, pp. 1004-1018. http://gdmltest.u-ga.fr/item/1176993721/