DeepAI
Log In Sign Up

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

06/01/2020
by   Tudor Manole, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/17/2022

Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models

We revisit convergence rates for maximum likelihood estimation (MLE) und...
01/11/2015

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

This paper studies identifiability and convergence behaviors for paramet...
01/27/2023

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

Dirichlet Process mixture models (DPMM) in combination with Gaussian ker...
09/05/2020

Identifying partners at sea on contrasting fisheries around the world

Here we present an approach to identify partners at sea based on fishing...
09/09/2016

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...
12/13/2018

Automatic Differentiation in Mixture Models

In this article, we discuss two specific classes of models - Gaussian Mi...
07/09/2019

Convergence Rates for Gaussian Mixtures of Experts

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

Code Repositories

Gaussian-mixture-twocomp

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