## The Annals of Statistics

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

### On the Convergence Properties of the EM Algorithm

#### 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 in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176346060

**Digital Object Identifier**

doi:10.1214/aos/1176346060

**Mathematical Reviews number (MathSciNet)**

MR684867

**Zentralblatt MATH identifier**

0517.62035

**JSTOR**

links.jstor.org

**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. Ann. Statist. 11 (1983), no. 1, 95--103. doi:10.1214/aos/1176346060. http://projecteuclid.org/euclid.aos/1176346060.