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Biometrika Advance Access originally published online on January 24, 2008
Biometrika 2008 95(1):139-147; doi:10.1093/biomet/asm088
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© 2008 Biometrika Trust

Articles

Bayesian and frequentist confidence intervals arising from empirical-type likelihoods

In Hong Chang

Department of Computer Science and Statistics, Chosun University, Gwangju 501-759, South Korea ihchang{at}chosun.ac.kr

Rahul Mukerjee

Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, Kolkata 700 104, India rmuk1{at}hotmail.com

Received for publication 1 August 2006. Revision received 1 June 2007.
  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.

Key Words: Edgeworth expansion • Frequentist coverage • Posterior coverage


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