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Likelihood Estimation with Normal Mixture Models

Author

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  • K. E. Basford
  • G. J. McLachlan

Abstract

We consider some of the problems associated with likelihood estimation in the context of a mixture of multivariate normal distributions. Unfortunately with mixture models, the likelihood equation usually has multiple roots and so there is the question of which root to choose. In the case of equal covariance matrices the choice of root is straightforward in the sense that the maximum likelihood estimator exists and is consistent. However, an example is presented to demonstrate that the adoption of a homoscedastic normal model in the presence of some heteroscedasticity can considerably influence the likelihood estimates, in particular of the mixing proportions, and hence the consequent clustering of the sample at hand.

Suggested Citation

  • K. E. Basford & G. J. McLachlan, 1985. "Likelihood Estimation with Normal Mixture Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 282-289, November.
    • Handle: RePEc:bla:jorssc:v:34:y:1985:i:3:p:282-289
    DOI: 10.2307/2347474
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    Cited by:

    1. Yongsung Joo & George Casella & James Hobert, 2010. "Bayesian model-based tight clustering for time course data," Computational Statistics, Springer, vol. 25(1), pages 17-38, March.
    2. Rania Hentati & Jean-Luc Prigent, 2011. "Portfolio Optimization Within Mixture Of Distributions," Post-Print hal-00607105, HAL.
    3. repec:dau:papers:123456789/13436 is not listed on IDEAS
    4. Hentati Rania & Prigent Jean-Luc, 2011. "On the maximization of financial performance measures within mixture models," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 63-80, March.
    5. Hentati-Kaffel, R. & Prigent, J.-L., 2016. "Optimal positioning in financial derivatives under mixture distributions," Economic Modelling, Elsevier, vol. 52(PA), pages 115-124.
    6. Alfonso García-Pérez, 2023. "A New Estimator: Median of the Distribution of the Mean in Robustness," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    7. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.
    8. Priyam Das, 2021. "Recursive Modified Pattern Search on High-Dimensional Simplex : A Blackbox Optimization Technique," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 440-483, November.
    9. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire, 2012. "Computational aspects of fitting mixture models via the expectation–maximization algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3843-3864.
    10. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    11. Harald Hannerz, 2001. "Manhood Trials and the Law of Mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 4(7), pages 185-202.

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