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Biometrika 2006 93(1):215-220; doi:10.1093/biomet/93.1.215
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© 2006 Biometrika Trust

Miscellanea

On Bartlett correction of empirical likelihood in the presence of nuisance parameters

Song Xi Chen1 and Hengjian Cui2

1 Department of Statistics, Iowa State University, Ames, Iowa 50011-1210, U.S.A. songchen{at}iastate.edu, 2 Department of Statistics and Financial Mathematics, Beijing Normal University, 100875, China hjcui{at}bnu.eud.cn

Lazar & Mykland (1999) showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be Bartlett-correctable. This paper shows that Bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest. We establish in the broad framework of estimating functions that the empirical likelihood is still Bartlett-correctable if the nuisance parameter is profiled out given the value of the parameter of interest.

Key Words: Bartlett correction; Empirical likelihood; Estimation equation; Nuisance parameter

Received August 2004. Revised March 2005.


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