A Proof of Strong Consistency of Maximum Likelihood Estimator for Independent Non-Identically Distributed Data
Statistics Theory
2025-01-14 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.2501.07257,
title = {A Proof of Strong Consistency of Maximum Likelihood Estimator for Independent Non-Identically Distributed Data},
author = {Ricardo Ferreira and Filipa Valdeira and Marta Guimarães and Cláudia Soares},
journal= {arXiv preprint arXiv:2501.07257},
year = {2025}
}