Expansions for the distribution of differentiable functionals of normalized sums of i.i.d. random vectors taking values in a separable Banach space are derived. Assuming that an $(r + 2)$th absolute moment exist, the CLT holds and the distribution of the $r$th derivative $r \geq 2$ of the functionals under the limiting Gaussian law admits a Lebesgue density which is sufficiently many times differentiable, expansions up to an order $O(n^{-r/2 + \varepsilon})$ hold. Applications to goodness-of-fit statistics, likelihood ratio statistics for discrete distribution families, bootstrapped confidence regions and functionals of the uniform empirical process are investigated.
Publié le : 1989-10-14
Classification:
Edgeworth expansions,
functional limit theorems in Banach spaces,
bootstrap,
goodness-of-fit statistics,
likelihood ratio statistics,
empirical processes,
60F17,
62E20
@article{1176991176,
author = {Gotze, F.},
title = {Edgeworth Expansions in Functional Limit Theorems},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1602-1634},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991176}
}
Gotze, F. Edgeworth Expansions in Functional Limit Theorems. Ann. Probab., Tome 17 (1989) no. 4, pp. 1602-1634. http://gdmltest.u-ga.fr/item/1176991176/