Multivariate saddlepoint approximations in tail probability and conditional inference

Abstract: We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study of endometrial cancer. The method contains less terms and is easier to implement than existing methods, while showing an accuracy comparable to those methods.