Asymptotic approximations for multivariate integrals with an application to multinormal probabilities
type: Item
instance of: scholarly article
title: Asymptotic approximations for multivariate integrals with an application to multinormal probabilities
zbMATH Open document ID: 0683.33003
DOI: 10.1016/0047-259X(89)90089-4
author: M. Hohenbichler
author: Karl W. Breitung
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: Generalizations of some known methods of asymptotic analysis are given. Known methods are based on the study of the local behavior of the integrand at some critical points which lie either in the interior of the integration domain or on twice continuously differentiable boundary. In the main result of the present paper the critical points are also allowed to lie on an edge or corner of the integration domain. The main result is applied to evaluate some multinormal probabilities.
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4118719
zbMATH Keywords: multinormal distribution
zbMATH Keywords: Laplace method
zbMATH Keywords: Mill's ratio
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
cites work: Q4092387
cites work: Q3687876
cites work: Q3913845
cites work: Asymptotics. II: Laplace's method for multiple integrals
cites work: Q4093215
cites work: Q5661032
cites work: An asymptotic expansion for the multivariate normal distribution and Mills' ratio
full work available at URL: 0047-259x(89)90089-4
OpenAlex ID: W2006172228
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description: scientific article; zbMATH DE number 4118719