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Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem

✍ Scribed by Olcay Arslan; Patrick D. L. Constable; John T. Kent

Publisher: Springer US
Year: 1993
Tongue: English
Weight: 449 KB
Volume: 3
Category: Article
ISSN: 0960-3174
DOI: 10.1007/bf00147772

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✦ Synopsis

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.

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