Saddlepoint approximations for likelihoods

Abstract

The saddlepoint approximation is a systematic method for converting a known generating function into an approximation for an unknown density function. Interpreted instead as an approximation to the unknown likelihood function, the saddlepoint approximation can be maximized to compute the saddlepoint MLE for a given observed value. This talk will explain how the saddlepoint approximation can be interpreted with a statistical lens, and describe a class of models with theoretical guarantees for the effect of using the saddlepoint MLE as a substitute for the unknown true MLE. The talk will also demonstrate new tools to simplify and automate the computation of saddlepoint MLEs and to quantitatively assess the amount of approximation error. Based on joint work with Godrick Oketch and Rachel Fewster.