Many important statistics can be written as functions of sample means of vector variables. A fundamental contribution to the Edgeworth expansion for functions of sample means was made by Bhattacharya and Ghosh. In their work the crucial Cramer $c$-condition is assumed on the joint distribution of all the components of the vector variable. However, in many practical situations, only one or a few of the components satisfy (conditionally) this condition while the rest do not (such a case is referred to as satisfying the partial Cramer $c$-condition). The purpose of this paper is to establish Edgeworth expansions for functions of sample means when only the partial Cramer $c$-condition is satisfied.
Publié le : 1991-09-14
Classification:
Asymptotic expansion,
central limit theorems,
Cramer-Edgeworth expansion,
function of sample means,
60F05,
62E20
@article{1176348250,
author = {Bai, Z. D. and Rao, C. Radhakrishna},
title = {Edgeworth Expansion of a Function of Sample Means},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 1295-1315},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348250}
}
Bai, Z. D.; Rao, C. Radhakrishna. Edgeworth Expansion of a Function of Sample Means. Ann. Statist., Tome 19 (1991) no. 1, pp. 1295-1315. http://gdmltest.u-ga.fr/item/1176348250/