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Constrained EM algorithm with projection method


  • Keiji Takai



This paper proposes a new step called the P-step to handle the linear or nonlinear equality constraint in addition to the conventional EM algorithm. This new step is easy to implement, first because only the first derivatives of the object function and the constraint function are necessary, and secondly, because the P-step is carried out after the conventional EM algorithm. The estimate sequence produced by our method enjoys a monotonic increase in the observed likelihood function. We apply the P-step in addition to the conventional EM algorithm to the two illustrative examples. The first example has a linear constraint function. The second has a nonlinear constraint function. We show finally that there exists a Kuhn–Tucker vector at the limit point produced by our method. Copyright Springer-Verlag 2012

Suggested Citation

  • Keiji Takai, 2012. "Constrained EM algorithm with projection method," Computational Statistics, Springer, vol. 27(4), pages 701-714, December.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:701-714
    DOI: 10.1007/s00180-011-0285-x

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    References listed on IDEAS

    1. Sik-Yum Lee & Sin-Yu Tsang, 1999. "Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 435-450, December.
    2. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    3. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    4. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
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