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Tail Exactness of Multivariate Saddlepoint Approximations
Author(s) -
BarndorffNielsen O. E.,
Kluppelberg C.
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00148
Subject(s) - mathematics , hessian matrix , exponential family , limit (mathematics) , multivariate statistics , central limit theorem , exponential function , domain (mathematical analysis) , boundary (topology) , combinatorics , mathematical analysis , statistics
We consider a log‐concave density f in R m satisfying certain weak conditions, particularly on the Hessian matrix of log f . For such a density, we prove tail exactness of the multivariate saddlepoint approximation. The proof is based on a local limit theorem for the exponential family generated by f . However, the result refers not to asymptotic behaviour under repeated sampling, but to a limiting property at the boundary of the domain of f . Our approach does not apply any complex analysis, but relies totally on convex analysis and exponential models arguments.