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The EM Algorithm

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  • McLachlan, Geoffrey J.
  • Krishnan, Thriyambakam
  • Ng, See Ket
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    Abstract

    The Expectation-Maximization (EM) algorithm is a broadly applicable approach to the iterative computation of maximum likelihood (ML) estimates, useful in a variety of incomplete-data problems. Maximum likelihood estimation and likelihood-based inference are of central importance in statistical theory and data analysis. Maximum likelihood estimation is a general-purpose method with attractive properties. It is the most-often used estimation technique in the frequentist framework; it is also relevant in the Bayesian framework (Chapter III.11). Often Bayesian solutions are justified with the help of likelihoods and maximum likelihood estimates (MLE), and Bayesian solutions are similar to penalized likelihood estimates. Maximum likelihood estimation is an ubiquitous technique and is used extensively in every area where statistical techniques are used. --

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    Bibliographic Info

    Paper provided by Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) in its series Papers with number 2004,24.

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    Date of creation: 2004
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    Handle: RePEc:zbw:caseps:200424

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    1. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    2. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 41(3-4), pages 379-388, January.
    3. M. Jamshidian & R. I. Jennrich, 2000. "Standard errors for EM estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 257-270.
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    Cited by:
    1. Ringle, Christian M., 2006. "Segmentation for path models and unobserved heterogeneity: The finite mixture partial least squares approach," MPRA Paper 10734, University Library of Munich, Germany.
    2. Qunqiang Feng & Hosam Mahmoud & Alois Panholzer, 2008. "Limit laws for the Randić index of random binary tree models," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 60(2), pages 319-343, June.
    3. Ke-Hai Yuan & Kentaro Hayashi, 2005. "On muthén’s maximum likelihood for two-level covariance structure models," Psychometrika, Springer, Springer, vol. 70(1), pages 147-167, March.
    4. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer, Springer, vol. 69(3), pages 437-457, September.
    5. Ingo Feinerer & Kurt Hornik & David Meyer, . "Text Mining Infrastructure in R," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 25(i05).
    6. Christophe Genolini & Bruno Falissard, 2010. "KmL: k-means for longitudinal data," Computational Statistics, Springer, Springer, vol. 25(2), pages 317-328, June.

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