Multivariate Saddlepoint Tail Probability Approximations

This paper presents a saddlepoint approximation to the cumulative distribution function of a random vector. The proposed approximation has accuracy comparable to that of existing expansions valid in two dimensions, and may be applied to random vectors of arbitrary length, subject only to the require...

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Bibliographic Details
Published in:The Annals of statistics 2003-02, Vol.31 (1), p.274-286
Main Author: Kolassa, John E.
Format: Article
Language:English
Subjects:
60E99
62E20
Approximation
Conditional probabilities
Conditional probability
Distribution theory
Error rates
Exact sciences and technology
Generating function
hypergeometric distribution
Inference
Integrands
lattice variable
Linear inference, regression
Mathematical integrals
Mathematical lattices
Mathematical vectors
Mathematics
Multivariate Analysis
Probabilities
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
tail probability
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Description
Summary:This paper presents a saddlepoint approximation to the cumulative distribution function of a random vector. The proposed approximation has accuracy comparable to that of existing expansions valid in two dimensions, and may be applied to random vectors of arbitrary length, subject only to the requirement that the distribution approximated either have a density or be confined to a lattice, and have a cumulant generating function. The result is derived by directly inverting the multivariate moment generating function. The result is applied to sufficient statistics from a regression model with exponential errors, and compared to an existing method in two dimensions. The result is also applied to multivariate inference from a data set arising from a case-control study of endometrial cancer.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1046294465