Maximum Likelihood Estimation via the ECM Algorithm: A General Framework

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. 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 completedata 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.

Confirmation of delayed canopy wilting QTLs from multiple soybean mapping populations

“…We estimated parameters in the QTL model, assuming that canopy wilting followed a normal distribution (Abdel-Haleem et al 2012;Charlson et al 2009), using the maximum likelihood approach (Weller 1986) and the EM algorithm (Meng and Rubin 1993). Single-factor ANOVA was used to determine if polymorphic markers were significantly (P < 0.05) associated with canopy wilting, and significant markers were used as cofactors in the standard CIM model (model 6, WinQTLCartographer, v. 2.5.010).…”

Bayesian analysis of quantile regression for censored dynamic panel data

“…The solution of this maximization can not be obtained in closed form, so that we follow Meng and Rubin (1993) and complete the M-step through a sequence of conditional maximizations. Specifically, the parameters are updated by the following two steps:…”

The ?-EM algorithm and its basic properties

“…Since the D-EM algorithm satisfies (12), it is a special case of the D-GEM algorithm. On the convergence of the D-GEM algorithm, we have two theorems.…”

“…This means that these vectors can be optimally selected by several independent optimization steps. The ECM algorithm (Expectation-Conditional Maximization algorithm) [12] is a method which exploits this property. This makes it possible to perform the maximization even if the total arg max is difficult to obtain.…”