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Bayesian and frequentist confidence intervals arising from empirical-type likelihoods

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  • In Hong Chang
  • Rahul Mukerjee

Abstract

For a general class of empirical-type likelihoods for the population mean, higher-order asymptotics are developed with a view to characterizing its members which allow, for any given prior, the existence of a confidence interval that has approximately correct posterior as well as frequentist coverage. In particular, it is seen that the usual empirical likelihood always allows such a confidence interval, while many of its variants proposed in the literature do not enjoy this property. An explicit form of the confidence interval is also given. Copyright 2008, Oxford University Press.

Suggested Citation

  • In Hong Chang & Rahul Mukerjee, 2008. "Bayesian and frequentist confidence intervals arising from empirical-type likelihoods," Biometrika, Biometrika Trust, vol. 95(1), pages 139-147.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:1:p:139-147
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    File URL: http://hdl.handle.net/10.1093/biomet/asm088
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    5. T. J. Sweeting, 1999. "On the construction of Bayes–confidence regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 849-861.
    6. 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.
    7. 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:

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    3. Rong Tang & Yun Yang, 2022. "Bayesian inference for risk minimization via exponentially tilted empirical likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1257-1286, September.
    4. Chang, In Hong & Mukerjee, Rahul, 2010. "Highest posterior density regions with approximate frequentist validity: The role of data-dependent priors," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1791-1797, December.
    5. F. Giummolè & V. Mameli & E. Ruli & L. Ventura, 2019. "Objective Bayesian inference with proper scoring rules," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 728-755, September.

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