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Statistica Sinica 21 (2011), 165-185





COMPOSITE LIKELIHOOD EM ALGORITHM

WITH APPLICATIONS

TO MULTIVARIATE HIDDEN MARKOV MODEL


Xin Gao and Peter X.-K. Song


York University and University of Michigan


Abstract: The method of composite likelihood is useful for dealing with estimation and inference in parametric models with high-dimensional data where the full likelihood approach renders computation intractable. We develop an extension of the EM algorithm in the framework of composite likelihood estimation given missing data or latent variables. We establish key theoretical properties of the composite likelihood EM (CLEM) algorithm: the ascent property, algorithmic convergence, and convergence rate. The proposed method is applied to estimate the transition probabilities in a multivariate hidden Markov model. Simulation studies are presented to demonstrate the empirical performance of the method. A time-course microarray data is analyzed using the proposed CLEM method to dissect the underlying gene regulatory network.



Key words and phrases: Composite likelihood, EM algorithm, hidden Markov model, latent variables, time-course microarray data.

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