On the approximate frequentist validity of the posterior quantiles of a parametric function: Results based on empirical and related likelihoods

Abstract

With reference to a wide class of empirical and related likelihoods, we study priors which ensure approximate frequentist validity of the posterior quantiles of a general parametric function. It is seen that no data-free prior entails such frequentist validity but, at least for the usual empirical likelihood, a data-dependent prior serves the purpose. Accounting for the nonlinearity of the parametric function of interest requires special attention in the derivation. A simulation study is seen to provide support, in finite samples, to our asymptotic results. � 2011 Sociedad de Estad�stica e Investigaci�n Operativa.