A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions
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TLDR
In this paper, the authors reformulated the maximum likelihood method of maximum likelihood in the case of a mixture of normal distributions into an optimization problem having a strongly consistent, global solution.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.read more
Citations
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References
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Mixture densities, maximum likelihood, and the EM algorithm
TL;DR: This work discusses the formulation and theoretical and practical properties of the EM algorithm, a specialization to the mixture density context of a general algorithm used to approximate maximum-likelihood estimates for incomplete data problems.
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
J. Kiefer,Jacob Wolfowitz +1 more
TL;DR: In this paper, the authors considered the problem of consisteently estimating 0 (as n --* X ), where the chance variables were assumed to be scalars, and the parameters 0 and ai may be vectors.
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Estimating the components of a mixture of normal distributions
TL;DR: In this article, the problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined, and the maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated.
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Estimating Mixtures of Normal Distributions and Switching Regressions
TL;DR: In this article, the authors introduced the "moment generating function estimator" which minimizes the sum of squares of differences between the theoretical and sample moment generating functions, and applied it to the Hamermesh model of wage bargain determination.