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Bayesian empirical likelihood

Author

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  • Nicole A. Lazar

Abstract

Research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods. This leads naturally to the possibility of using empirical likelihood as the basis for Bayesian inference. Different ways in which this goal might be accomplished are considered. The validity of the resultant posterior inferences is examined, as are frequentist properties of the Bayesian empirical likelihood intervals. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:319-326
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    Citations

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    Cited by:

    1. Sanjay Chaudhuri & Malay Ghosh, 2011. "Empirical likelihood for small area estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 473-480.
    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. repec:bla:jorssb:v:79:y:2017:i:1:p:293-320 is not listed on IDEAS
    4. Rahul Mukerjee & Ling-Yau Chan, 2009. "Confidence intervals based on empirical statistics: existence of a probability matching prior and connection with frequentist Bartlett adjustability," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 271-282, August.
    5. J. N. K. Rao & Changbao Wu, 2010. "Bayesian pseudo-empirical-likelihood intervals for complex surveys," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 533-544.
    6. Albert Vexler & Wan-Min Tsai & Alan D. Hutson, 2014. "A Simple Density-Based Empirical Likelihood Ratio Test for Independence," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 158-169, February.
    7. Ventura, Laura & Racugno, Walter, 2012. "On interval and point estimators based on a penalization of the modified profile likelihood," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1285-1289.
    8. Zhichao Liu & Catherine Forbes & Heather Anderson, 2017. "Robust Bayesian exponentially tilted empirical likelihood method," Monash Econometrics and Business Statistics Working Papers 21/17, Monash University, Department of Econometrics and Business Statistics.
    9. repec:eee:macchp:v2-527 is not listed on IDEAS
    10. 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.
    11. Lin, Lu & Tan, Lin, 2008. "Proper Bayesian estimating equation based on Hilbert space method," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1119-1127, July.
    12. Lehmann, Bruce N., 2009. "The role of beliefs in inference for rational expectations models," Journal of Econometrics, Elsevier, vol. 150(2), pages 322-331, June.
    13. Albert Vexler & Young Min Kim & Jihnhee Yu & Nicole A. Lazar & Alan D. Hutson, 2014. "Computing Critical Values of Exact Tests by Incorporating Monte Carlo Simulations Combined with Statistical Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1013-1030, December.
    14. 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.
    15. repec:ags:stataj:259860 is not listed on IDEAS
    16. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    17. 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.
    18. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    19. Zhang, Yan-Qing & Tang, Nian-Sheng, 2017. "Bayesian local influence analysis of general estimating equations with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 184-200.

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