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A hybrid EM/Gauss-Newton algorithm for maximum likelihood in mixture distributions

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Abstract

A faster alternative to the EM algorithm in finite mixture distributions is described, which alternates EM iterations with Gauss-Newton iterations using the observed information matrix. At the expense of modest additional analytical effort in obtaining the observed information, the hybrid algorithm reduces the computing time required and provides asymptotic standard errors at convergence. The algorithm is illustrated on the two-component normal mixture.

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Authors and Affiliations

  1. Department of Mathematics, University of Western Australia, Western Australia, Australia

    Murray Aitkin

  2. Department of Statistics, University of Newcastle Upon Tyne, Newcastle Upon Tyne, UK

    Murray Aitkin

  3. Department of Epidemiology and Biostatistics, School of Public Health, Curtin University of Technology, Bentley, Western Australia, Australia

    Irit Aitkin

Authors
  1. Murray Aitkin
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  2. Irit Aitkin
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Aitkin, M., Aitkin, I. A hybrid EM/Gauss-Newton algorithm for maximum likelihood in mixture distributions. Stat Comput 6, 127–130 (1996). https://doi.org/10.1007/BF00162523

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