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- Title
Degeneracy in the Maximum Likelihood Estimation of Univariate Gaussian Mixtures for Grouped Data and Behaviour of the EM Algorithm.
- Authors
Biernacki, Christophe
- Abstract
In the context of the univariate Gaussian mixture with grouped data, it is shown that the global maximum of the likelihood may correspond to a situation where a Dirac lies in any non-empty interval. Existence of a domain of attraction near such a maximizer is discussed and we establish that the expectation-maximization (EM) iterates move extremely slowly inside this domain. These theoretical results are illustrated both by some Monte-Carlo experiments and by a real data set. To help practitioners identify and discard these potentially dangerous degenerate maximizers, a specific stopping rule for EM is proposed.
- Subjects
GAUSSIAN measures; MAXIMUM likelihood statistics; EXPECTATION-maximization algorithms; ALGORITHMS; STOCHASTIC processes; DIRAC equation; PARTIAL differential equations; QUANTUM field theory; STOCHASTIC convergence
- Publication
Scandinavian Journal of Statistics, 2007, Vol 34, Issue 3, p569
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2006.00553.x