The Annals of Probability

On Edgeworth Expansions in Banach Spaces

F. Gotze

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Abstract

In this paper we define a generalization of Edgeworth expansions for the expectation of functions of normalized sums of i.i.d. Banach space valued random vectors. These expansions are valid up to $0(n^{-(s - 2)/2})$ for functions with $3(s - 2)$ bounded Frechet derivatives and random vectors with finite $s^{th}$ absolute moment.

Article information

Source
Ann. Probab., Volume 9, Number 5 (1981), 852-859.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994312

Digital Object Identifier
doi:10.1214/aop/1176994312

Mathematical Reviews number (MathSciNet)
MR628877

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

Keywords
Edgeworth expansions Central Limit Theorem in Banach spaces

Citation

Gotze, F. On Edgeworth Expansions in Banach Spaces. Ann. Probab. 9 (1981), no. 5, 852--859. doi:10.1214/aop/1176994312. https://projecteuclid.org/euclid.aop/1176994312


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