The Annals of Statistics

On the Convergence Properties of the EM Algorithm

C. F. Jeff Wu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist. Volume 11, Number 1 (1983), 95-103.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176346060

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176346060

Mathematical Reviews number (MathSciNet)
MR684867

Zentralblatt MATH identifier
0517.62035

Subjects
Primary: 62F10: Point estimation
Secondary: 90C30: Nonlinear programming

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

Citation

Wu, C. F. Jeff. On the Convergence Properties of the EM Algorithm. The Annals of Statistics 11 (1983), no. 1, 95--103. doi:10.1214/aos/1176346060. http://projecteuclid.org/euclid.aos/1176346060.


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