ECM algorithms that converge at the rate of EM

• Published in: Biometrika Vol. 87; no. 3; pp. 651 - 662
• Main Authors: Sexton, J, Swensen, AR
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.09.2000; Biometrika Trust; Oxford Publishing Limited (England)
• Subjects: Algorithms; conjugate directions algorithm; Covariance matrices; Datasets; Distribution theory; ECM algorithm; Economic models; EM algorithm; Exact sciences and technology; Markov chains; Mathematical foundations; Mathematical vectors; Mathematics; Matrices; Maximum likelihood estimators; Missing data; orthogonal parameters; Probability and statistics; rate of convergence; Sciences and techniques of general use; Statistics; Time series models; Conjugate gradient method; Loglikelihood; Orthogonal parameter; Existence theorem; Statistical theory; Probability distribution; Missing data; Distribution function; Convergence rate; Approximation theory; Conjugate directional algorithm; Maximum likelihood; EM algorithm; Likelihood function
• ISSN: 0006-3444; 1464-3510; 1464-3510
• DOI: 10.1093/biomet/87.3.651

We show that the ECM algorithm can always be constructed to converge at the same or approximately the same rate as the EM algorithm. The construction is based on the well-known conjugate directions algorithm. This result both suggests ways of speeding up the convergence of ECM and provides a simple way of identifying cases where the simplicity and stability of ECM over EM is attained at effectively no loss in convergence speed. Three examples are given.