Multivariate saddlepoint approximations in tail probability and conditional inference

TL;DR

This paper develops multivariate saddlepoint approximation methods for tail probabilities and conditional inference, applicable to continuous and lattice variables, with demonstrated accuracy and ease of implementation.

Contribution

It extends saddlepoint approximations to multivariate and conditional cases, simplifying implementation while maintaining accuracy.

Findings

Accurate tail probability approximations for multivariate data

Applicable to both continuous and lattice variables

Simpler and more efficient than existing methods

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.