Log In Sign Up

Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models

by   Tudor Manole, et al.

We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of the mixture are known and fixed, but make no separation assumption on the underlying mixture components. A phase transition is shown to exist in the optimal parameter estimation rate, depending on whether or not the mixture is balanced. Key to our analysis is a careful study of the dependence between the parameters of location-scale Gaussian mixture models, as captured through systems of polynomial equalities and inequalities whose solution set drives the rates we obtain. A simulation study illustrates the theoretical findings of this work.


page 1

page 2

page 3

page 4


Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models

We revisit convergence rates for maximum likelihood estimation (MLE) und...

Identifiability and optimal rates of convergence for parameters of multiple types in finite mixtures

This paper studies identifiability and convergence behaviors for paramet...

On Excess Mass Behavior in Gaussian Mixture Models with Orlicz-Wasserstein Distances

Dirichlet Process mixture models (DPMM) in combination with Gaussian ker...

Identifying partners at sea on contrasting fisheries around the world

Here we present an approach to identify partners at sea based on fishing...

Singularity structures and impacts on parameter estimation in finite mixtures of distributions

Singularities of a statistical model are the elements of the model's par...

Automatic Differentiation in Mixture Models

In this article, we discuss two specific classes of models - Gaussian Mi...

Convergence Rates for Gaussian Mixtures of Experts

We provide a theoretical treatment of over-specified Gaussian mixtures o...

Code Repositories


Code repository for reproducing the simulation study in the paper "Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models".

view repo