Composite likelihood approach to finite normal mixture models
A composite likelihood consists of a combination of valid likelihood objects. It is shown to be an good and practical alternative to the ordinary full likelihood when the full likelihood is intractable, or difficult to evaluate due to complex dependencies. The composite likelihood approach has demonstrated its advantage in a number of applications. For a few but important cases the composite likelihood is fully efficient with identical estimators compared to the full likelihood.
In this talk, we propose to use composite likelihood method for analyzing multivariate normal mixture models. Some statistical properties of the composite likelihood estimator, consistency and asymptotic normality, are established. A composite likelihood EM algorithm is used to maximize the penalized pairwise log-likelihood function. We prove that the CL-EM algorithm satisfies the ascent property and converges to a stationary point of the objective function. Simulation studies are presented to demonstrate the performance of the method. A comparison with the ordinary likelihood is given.