A Proof of Strong Consistency of Maximum Likelihood Estimator for Independent Non-Identically Distributed Data

TL;DR

This paper provides a general proof of the strong consistency of the maximum likelihood estimator for independent non-identically distributed data, under specific assumptions, extending classical results and applying to orbit determination.

Contribution

It offers a new, general proof of strong consistency for MLE in i.n.i.d data, based on classical works, and demonstrates its application to orbit determination.

Findings

Proves strong consistency of MLE for i.n.i.d data under specific assumptions

Extends classical consistency results to more general data settings

Applies the theoretical result to orbit determination problems

Abstract

We give a general proof of the strong consistency of the Maximum Likelihood Estimator for the case of independent non-identically distributed (i.n.i.d) data, assuming that the density functions of the random variables follow a particular set of assumptions. Our proof is based on the works of Wald~\cite{wald1949note}, Goel~\cite{goel1974note}, and Ferguson~\cite{ferguson2017course}. We use this result to prove the strong consistency of a Maximum Likelihood Estimator for Orbit Determination.