Rahul Mukerjee

Indian Institute of Management Calcutta

Highest posterior density regions based on empirical-type likelihoods: Role of data-dependent priors

We consider the Bayesian versus frequentist interface with reference to a very general class of empirical-type likelihoods which includes the usual empirical likelihood and all its major variants proposed in the literature. Probability matching priors play a key role in this context. It is known that none of these likelihoods admits a data-free probability matching prior for the highest posterior density region. We show that at least for the usual empirical likelihood this problem can be resolved if data-dependent priors are entertained. Necessary higher order asymptotics are developed for this purpose. The theoretical results are supported by a simulation study.