Reference priors based on composite likelihoods

In this paper we propose reference priors obtained by maximizing the average alpha-divergence from the posterior distribution, when the latter is computed using a composite likelihood. Composite posterior distributions have already been considered in Pauli et al. (2011) and Ribatet et al. (2012), when a full likelihood for the data is too complex or even not available. The use of a curvature corrected composite posterior distribution, as in Ribatet et al. (2012), allows to apply the method in Liu et al. (2014) for maximizing the asymptotic Bayes risk associated to an alpha-divergence. The result is a Jeffreys type prior that is proportional to the square root of the determinant of the Godambe information matrix.