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Biometrika 2002 89(4):958-961; doi:10.1093/biomet/89.4.958
© 2002 by Biometrika Trust
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Miscellanea

A note on a partial empirical likelihood

F.Zou1 and J.P. Fine2

1 Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.Afzou{at}bios.unc.edu 2 Department of Statistics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.fine{at}stat.wisc.edu

A partial profile empirical likelihood for a semiparametric mixture model (Zou et al., 2002) is shown to originate in a conditional likelihood involving additional nuisance parameters. The partial likelihood is the conditional likelihood with the nuisance parameters replaced by their estimators from the full likelihood.The conditional likelihood suggests alternative estimators. We demonstrate that the partial likelihood estimator is more efficient than an estimator for which the nuisance parameters are known. The practical implications of this counter-intuitive result are discussed.

Key Words: Information matrix; Maximum likelihood; Mixture label; Nuisance parameter; Quantitative trait locus

Received January 2002. Revised June 2002


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