Tail Exactness of Multivariate Saddlepoint Approximations

O. E. Barndorff‐Nielsen and C. Kluppelberg
Authors registered in the RePEc Author Service: Ole E. Barndorff-Nielsen

Scandinavian Journal of Statistics, 1999, vol. 26, issue 2, 253-264

Abstract: We consider a log‐concave density f in Rm 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.

Date: 1999
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