A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions

Open Access

1 June 1985

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 13 (2) , 795-800
https://doi.org/10.1214/aos/1176349557

Abstract

The method of maximum likelihood leads to an ill-posed optimization problem in the case of a mixture of normal distributions. Estimation in the univariate case is reformulated using simple constraints into an optimization problem having a strongly consistent, global solution.

Keywords

CONSISTENCY
MAXIMUM-LIKELIHOOD ESTIMATION
NORMAL MIXTURE DENSITIES

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