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Maximum likelihood estimation via the ECM algorithm: A general framework. (English) Zbl 0778.62022
Summary: Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the \(M\)-step is computationally unattractive. In many cases, however, complete-data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated.
We introduce a class of generalized EM algorithms, which we call the ECM algorithm, for Expectation/Conditional Maximization (CM), that takes advantage of the simplicity of complete-data conditional maximum likelihood estimation by replacing a complicated \(M\)-step of EM with several computationally simpler CM-steps. We show that the ECM algorithm shares all the appealing convergence properties of EM, such as always increasing the likelihood, and present several illustrative examples.

62F10 Point estimation
65C99 Probabilistic methods, stochastic differential equations
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