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Estimation of Mixing Proportions: A Case Study

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  • K. Do
  • G. J. McLachlan

Abstract

Observations are taken from a mixture of several populations and the problem is to estimate the unknown mixing proportions on the basis of this sample which is unclassified; that is, it is not known to which population an observation belongs. There are reference data of known origin available separately from each of the populations for the purposes of estimation of the unknown population parameters. Two approaches to this problem are illustrated by the presentation of a case study involving an unclassified sample of n = 1107 four‐dimensional observations taken from a mixture of seven populations. The usefulness of atypicality indices for assessing whether an unclassified observation comes from one of the specified populations is exhibited.

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  • K. Do & G. J. McLachlan, 1984. "Estimation of Mixing Proportions: A Case Study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 134-140, June.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:2:p:134-140
    DOI: 10.2307/2347437
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    Cited by:

    1. Susko, Edward, 2003. "Weighted tests of homogeneity for testing the number of components in a mixture," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 367-378, January.
    2. Mkhadri, Abdallah & Nasroallah, Abdelaziz, 1997. "Note on classification and proportion estimation," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 151-158, June.
    3. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.

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