On the Convergence Properties of the EM Algorithm

by: Jeff FJ Wu

The Annals of Statistics, Vol. 11, No. 1. (1983), pp. 95-103.

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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{citeulike:117580, 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.}, author = {Wu, Jeff F. J. }, citeulike-article-id = {117580}, journal = {The Annals of Statistics}, keywords = {em}, number = {1}, pages = {95--103}, posted-at = {2008-02-19 19:01:46}, priority = {2}, title = {On the Convergence Properties of the EM Algorithm}, url = {http://www.jstor.org/stable/2240463}, volume = {11}, year = {1983} }

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TY - JOUR ID - citeulike:117580 L3 - citeulike-article-id:117580 TI - On the Convergence Properties of the EM Algorithm JF - The Annals of Statistics VL - 11 IS - 1 SP - 95 EP - 103 N2 - 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. KW - em AU - Wu, Jeff PY - 1983/// UR - http://www.jstor.org/stable/2240463 ER -

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