Consistency of the Maximum Likelihood Estimator of Evolutionary Tree

TL;DR

This paper examines the theoretical consistency of maximum likelihood estimators for evolutionary trees, addressing gaps in existing proofs and discussing the applicability of Wald's classical proof.

Contribution

It critically analyzes existing proofs of MLE consistency for evolutionary trees and clarifies the conditions under which Wald's proof applies.

Findings

Identifies shortcomings in previous proofs

Discusses the applicability of Wald's proof

Provides insights into the consistency of MLE for evolutionary trees

Abstract

Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical proof of consistency by Wald holds for the MLE of evolutionary tree. Other proofs of consistency under various models were also proposed. Here we will discuss some shortcomings in some of these proofs and comment on the applicability of Wald's proof.