Seminar by Yanbo Tang

Randomly weighted composite likelihoods

The definition of the composite likelihood is extended to include random data-dependent weights and the asymptotic properties under this new definition; this new class is named randomly weighted composite likelihoods.

We propose general regularity conditions sufficient for consistency and asymptotic normality of the estimators based on the randomly weighted composite likelihood and a Bernstein von-Mises theorem on the posterior obtained from the Bayesian composite likelihood.  The developed theorems allows us to analyze several existing objects in the literature such as powered likelihoods, weighted likelihood for covariate shift and coreset methods. We focus our examples on the marginal composite likelihood and the pairwise composite likelihood, but the general theorems are applicable to all composite likelihoods -- although checking the necessary conditions may be difficult.