On Non Asymptotic Expansion of the MME in the Case of Poisson Observations

TL;DR

This paper develops non-asymptotic stochastic expansions for the method of moments estimator in inhomogeneous Poisson process parameter estimation, providing detailed moment and distribution function expansions.

Contribution

It introduces non-asymptotic stochastic expansions for the MME in inhomogeneous Poisson processes, enhancing understanding of estimator behavior beyond asymptotic approximations.

Findings

Derived non-asymptotic stochastic expansion of the MME

Obtained expansion of moments and distribution function

Applied expansions to several examples

Abstract

The problem of parameter estimation by observations of inhomogeneous Poisson processes is considered. The method of moments estimator is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of this estimator and the expansion of the distribution function. The stochastic expansion, expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are considered.