Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima
type: Item
instance of: scholarly article
title: Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima
zbMATH Open document ID: 0608.60018
DOI: 10.1007/BF00319983
author: Erwin Bolthausen
publication date: 1987-01-01T00:00:00Z
review text: We consider expressions of the form \(Z_ n=E(\exp (nF(S_ n/n))\) where \(S_ n\) is the sum of n i.i.d. random vectors with values in a Banach space and F is a smooth real valued function. By results of Donsker- Varadhan and Bahadur-Zabell one knows that lim(1/n)log \(Z_ n=\sup _ x(F(x)-h(x))b_ F\) where h is the so-called entropy function. In part I [ibid. 72, 305-318 (1986; Zbl 0572.60007)] a more precise evaluation of \(Z_ n\) is given in the case where there was a unique point maximizing F-h and the curvature at the maximum was nonvanishing. The present paper treats the more delicate problem where these conditions fail to hold.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3984206
zbMATH Keywords: Laplace approximations
zbMATH Keywords: degenerate maxima
zbMATH Keywords: manifolds of maxima
zbMATH Keywords: entropy function
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00319983
OpenAlex ID: W3091777984
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3984206