Open Access
March, 1983 On the Convergence Properties of the EM Algorithm
C. F. Jeff Wu
Ann. Statist. 11(1): 95-103 (March, 1983). DOI: 10.1214/aos/1176346060


Two convergence aspects of the EM algorithm are studied: (i) does the EM algorithm find a local maximum or a stationary value of the (incomplete-data) likelihood function? (ii) does the sequence of parameter estimates generated by EM converge? Several convergence results are obtained under conditions that are applicable to many practical situations. Two useful special cases are: (a) if the unobserved complete-data specification can be described by a curved exponential family with compact parameter space, all the limit points of any EM sequence are stationary points of the likelihood function; (b) if the likelihood function is unimodal and a certain differentiability condition is satisfied, then any EM sequence converges to the unique maximum likelihood estimate. A list of key properties of the algorithm is included.


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C. F. Jeff Wu. "On the Convergence Properties of the EM Algorithm." Ann. Statist. 11 (1) 95 - 103, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0517.62035
MathSciNet: MR684867
Digital Object Identifier: 10.1214/aos/1176346060

Primary: 62F10
Secondary: 90C30

Keywords: curved exponential family , EM algorithm , GEM algorithm , incomplete data , maximum likelihood estimate

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • March, 1983
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