A fifth order expansion for the distribution function of the maximum likelihood estimator

TL;DR

This paper extends the theoretical understanding of the maximum likelihood estimator by deriving fifth order expansions for its distribution function, providing more precise approximations.

Contribution

The paper introduces fifth order expansions for the distribution function of the maximum likelihood estimator, advancing previous lower-order results.

Findings

Derived fifth order expansion formulas

Simplified proofs based on earlier methods

Enhanced accuracy in distribution approximation

Abstract

In this paper, expansions for the maximum likelihood estimator of location and its distribution funtion are extended to fifth order. Since the proofs are straightforward extentions of proofs given in earlier papers for orders less than the fifth, they are not given here. The purpose of the paper is mainly to present the higher order expansions.