Laplace approximations for sums of independent random vectors

Shigeo Kusuoka; Song Liang

doi:10.1007/PL00008727

Laplace approximations for sums of independent random vectors

Shigeo Kusuoka, Song Liang

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let X_i, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B → R. Under a central limit theorem assumption, an asymptotic evaluation of Z_n = E (exp (nΦ(Σⁿ_i=1 X_i/n))), up to a factor (1 + 0(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption.

Original language	English
Pages (from-to)	221-238
Number of pages	18
Journal	Probability Theory and Related Fields
Volume	116
Issue number	2
DOIs	https://doi.org/10.1007/PL00008727
Publication status	Published - 2000 Feb
Externally published	Yes

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/PL00008727

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abstract = "Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B → R. Under a central limit theorem assumption, an asymptotic evaluation of Zn = E (exp (nΦ(Σni=1 Xi/n))), up to a factor (1 + 0(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption.",

author = "Shigeo Kusuoka and Song Liang",

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AU - Liang, Song

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AB - Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B → R. Under a central limit theorem assumption, an asymptotic evaluation of Zn = E (exp (nΦ(Σni=1 Xi/n))), up to a factor (1 + 0(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption.

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ER -

Laplace approximations for sums of independent random vectors

Abstract

ASJC Scopus subject areas

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