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A composite likelihood consists of a combination of valid likelihood objects, and in particular it is of typical interest to adopt lower dimensional marginal likelihoods. Composite marginal likelihood appears to be an attractive alternative for modeling complex data, and has received increasing attention in handling high dimensional data sets when the joint distribution is computationally difficult to evaluate, or intractable due to complex structure of dependence. We present some aspects of methodological development in composite likelihood inference. The resulting estimator enjoys desirable asymptotic properties such as consistency and asymptotic normality. Composite likelihood based test statistics and their asymptotic distributions are summarized. Higher order asymptotic properties of the signed composite likelihood root statistic are explored. Moreover, we aim to compare accuracy and efficiency of composite likelihood estimation relative to estimation based on ordinary likelihood. Analytical and simulation results are presented for different models, which include multivariate normal distributions, times series model, and correlated binary data.

A composite likelihood consists of a combination of valid likelihood objects, and in particular it is of typical interest to adopt lower dimensional marginal likelihoods. Composite marginal likelihood appears to be an attractive alternative for modeling complex data, and has received increasing attention in handling high dimensional data sets when the joint distribution is computationally difficult to evaluate, or intractable due to complex structure of dependence. We present some aspects of methodological development in composite likelihood inference. The resulting estimator enjoys desirable asymptotic properties such as consistency and asymptotic normality. Composite likelihood based test statistics and their asymptotic distributions are summarized. Higher order asymptotic properties of the signed composite likelihood root statistic are explored. Moreover, we aim to compare accuracy and efficiency of composite likelihood estimation relative to estimation based on ordinary likelihood. Analytical and simulation results are presented for different models, which include multivariate normal distributions, times series model, and correlated binary data.