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Expected lengths of confidence intervals based on empirical discrepancy statistics

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  • Kai-tai Fang
  • Rahul Mukerjee

Abstract

We consider a very general class of empirical discrepancy statistics that includes the Cressie--Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order asymptotics for expected lengths of associated confidence intervals are investigated. An explicit formula is worked out and its use for comparative purposes is discussed. It is seen that the empirical likelihood ratio statistic, which enjoys interesting second-order power properties, loses much of its edge under the present criterion. Copyright 2005, Oxford University Press.

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  • 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.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:499-503
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    File URL: http://hdl.handle.net/10.1093/biomet/92.2.499
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    1. 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.
    2. Sanjay Chaudhuri & Malay Ghosh, 2011. "Empirical likelihood for small area estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 473-480.
    3. 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.
    4. 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.
    5. In Chang & Rahul Mukerjee, 2006. "Asymptotic Results on a General Class of Empirical Statistics: Power and Confidence Interval Properties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 427-440, September.
    6. 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.

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