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Matching posterior and frequentist cumulative distribution functions with empirical-type likelihoods in the multiparameter case

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  • Chang, In Hong
  • Mukerjee, Rahul

Abstract

We consider a general class of empirical-type likelihoods for a vector-valued population mean. Members of the class that admit a matching prior, in a higher order asymptotic sense, for the posterior and frequentist cumulative distribution functions are characterized. The results are compared and contrasted with those on posterior quantiles in the scalar-valued case.

Suggested Citation

  • Chang, In Hong & Mukerjee, Rahul, 2008. "Matching posterior and frequentist cumulative distribution functions with empirical-type likelihoods in the multiparameter case," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2793-2797, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2793-2797
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    References listed on IDEAS

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    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    2. Kai-Tai Fang & Rahul Mukerjee, 2006. "Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics," Biometrika, Biometrika Trust, vol. 93(3), pages 723-733, September.
    3. Francesco Bravo, 2003. "Second-order power comparisons for a class of nonparametric likelihood-based tests," Biometrika, Biometrika Trust, vol. 90(4), pages 881-890, December.
    4. Kai-tai Fang & Rahul Mukerjee, 2005. "Expected lengths of confidence intervals based on empirical discrepancy statistics," Biometrika, Biometrika Trust, vol. 92(2), pages 499-503, June.
    5. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    6. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
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    Cited by:

    1. In Chang & Rahul Mukerjee, 2012. "On the approximate frequentist validity of the posterior quantiles of a parametric function: results based on empirical and related likelihoods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 156-169, March.

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