Let $S_n$ denote the $n$th normalized partial sum of a sequence of mean zero, weakly dependent random vectors. This paper gives asymptotic expansions for $Ef(S_n)$ under weaker moment conditions than those of Gotze and Hipp (1983). It is also shown that an expansion for $Ef(S_n)$ with an error term $o(n^{-(s - 2)/2})$ is valid without any Cramer-type condition, if $f$ has partial derivatives of order $(s - 1)$ only. This settles a conjecture of Gotze and Hipp in their 1983 paper.
@article{1176989267,
author = {Lahiri, Soumendra Nath},
title = {Refinements in Asymptotic Expansions for Sums of Weakly Dependent Random Vectors},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 791-799},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989267}
}
Lahiri, Soumendra Nath. Refinements in Asymptotic Expansions for Sums of Weakly Dependent Random Vectors. Ann. Probab., Tome 21 (1993) no. 4, pp. 791-799. http://gdmltest.u-ga.fr/item/1176989267/