Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small

DOI10.3150/bj/1165269148zbMath1117.62025arXivmath/0605148OpenAlexW2054231149MaRDI QIDQ2642801

Kentaro Tanaka, Akimichi Takemura

Publication date: 5 September 2007

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605148

zbMATH Keywords

consistencymaximum likelihood estimatormixture distribution

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Parametric inference under constraints (62F30)

Related Items (16)

A new look at the inverse Gaussian distribution with applications to insurance and economic data ⋮ Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers ⋮ Estimation and computations for Gaussian mixtures with uniform noise under separation constraints ⋮ Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small ⋮ Semiparametric mixture: continuous scale mixture approach ⋮ Asymptotic properties of the estimator for a finite mixture of exponential dispersion models ⋮ Strong consistency of the MLE under two-parameter Gamma mixture models with a structural scale parameter ⋮ Eigenvalues and constraints in mixture modeling: geometric and computational issues ⋮ A data driven equivariant approach to constrained Gaussian mixture modeling ⋮ A computational strategy for doubly smoothed MLE exemplified in the normal mixture model ⋮ A CLASSICAL INVARIANCE APPROACH TO THE NORMAL MIXTURE PROBLEM ⋮ Consistency of the penalized MLE for two-parameter gamma mixture models ⋮ Root selection in normal mixture models ⋮ Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions ⋮ Inference of finite mixture models and the effect of binning ⋮ Consistency of the MLE under a two-parameter gamma mixture model with a structural shape parameter

Cites Work

• Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small
• A constrained formulation of maximum-likelihood estimation for normal mixture distributions
• Note on the consistency of the maximum likelihood estimate for nonidentifiable distributions
• Nonparametric maximum likelihood estimation by the method of sieves
• Rates of convergence for the Gaussian mixture sieve.
• Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities.
• Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small
• Finite mixture models
• Note on the Consistency of the Maximum Likelihood Estimate
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