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October, 1989 Edgeworth Expansions in Functional Limit Theorems
F. Gotze
Ann. Probab. 17(4): 1602-1634 (October, 1989). DOI: 10.1214/aop/1176991176


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.


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F. Gotze. "Edgeworth Expansions in Functional Limit Theorems." Ann. Probab. 17 (4) 1602 - 1634, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0689.60038
MathSciNet: MR1048948
Digital Object Identifier: 10.1214/aop/1176991176

Primary: 60F17
Secondary: 62E20

Keywords: bootstrap , Edgeworth expansions , Empirical processes , functional limit theorems in Banach spaces , goodness-of-fit statistics , likelihood ratio statistics

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 4 • October, 1989
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