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

• Autores: In Hong Chang, Rahul Mukerjee
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 21, Nº. 1, 2012, págs. 156-169
• Idioma: inglés
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• Resumen

  • 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.