Summary
The paper gives a brief history of the estimation problem for mixtures of gaussian populations. The classical maximum likelihood approach is not appropriate since the likelihood function is unbounded at each sample point. However, this does not seem to cause serious problems when iterative methods are used on a computer. This phenomenon is partially explained by the conditional likelihood approach taken in this paper. In addition, the conditional likelihood approach leads to consistent, asymptotically normal and efficient estimators for the parameters of the mixture. The results of a Monte Carlo study are reported for the univariate case and these show that the procedures provide reasonable estimators for small sample sizes. The methods are then extended to mixtures of multivariate gaussian populations.
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Policello, G.E. (1981). Conditional Maximum Likelihood Estimation in Gaussian Mixtures. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_9
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DOI: https://doi.org/10.1007/978-94-009-8552-0_9
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