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We extend known saddlepoint tail probability approximations to multivariatecases, including multivariate conditional cases. Our approximation applies toboth continuous and lattice variables, and requires the existence of a cumulantgenerating function. The method is applied to some examples, including a realdata set from a case-control study of endometrial cancer. The method containsless terms and is easier to implement than existing methods, while showing anaccuracy comparable to those methods.

Multivariate saddlepoint approximations in tail probability and conditional inference