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Biometrika 2005 92(2):499-503; doi:10.1093/biomet/92.2.499
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© 2005 Biometrika Trust

Miscellanea

Expected lengths of confidence intervals based on empirical discrepancy statistics

Kai-tai Fang1 and Rahul Mukerjee2

1 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China ktfang{at}math.hkbu.edu.hk, 2 Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, Kolkata 700 104, India rmuk1{at}hotmail.com

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.

Key Words: Cressie–Read discrepancy; Edgeworth expansion; Empirical likelihood; Minimaxity

Received June 2004. Revised October 2004.


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[Abstract] [PDF]


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