Simple error bounds for the multivariate Laplace approximation under weak local assumptions

TL;DR

This paper establishes new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions, broadening its applicability and removing unnecessary conditions from previous results.

Contribution

It generalizes existing bounds for the multivariate Laplace approximation by weakening assumptions and providing a broader range of validity, including an application to Dixon's identity extension.

Findings

New bounds for multivariate Laplace approximation under weak assumptions

Broader validity range for approximation bounds

Application to integral extension of Dixon's identity

Abstract

The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is presented. The paper both generalizes and complements recent results by Inglot and Majerski and removes their superfluous assumption on vanishing of the third order partial derivatives of the exponent function.