The method of composite likelihood is useful to deal with estimation and inference in parametric models with high-dimensional data, where the full likelihood approach renders to intractable computational complexity. We develop an extension of the EM algorithm in the framework of composite likelihood estimation in the presence of missing data or latent variables. We establish three key theoretical properties of the composite likelihood EM (CLEM) algorithm, including the ascent property, the algorithmic convergence and the convergence rate. The proposed method is applied to estimate the transition probabilities in 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.
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