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Biometrika 1998 85(3):535-547; doi:10.1093/biomet/85.3.535
© 1998 by Biometrika Trust
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Empirical likelihood as a goodness-of-fit measure

KEITH A. BAGGERLY

Department of Statistics-MS 138, Rice University 61 00 Main Street, Houston, Texas 77005, U.S.A.kabagg{at}stat.rice.edu

The method of empirical likelihood can be viewed as one of allocating probabilities to an n-cell contingency table so as to minimise a goodness-of-fit criterion. It is shown that, when the Cressie-Read power-divergence statistic is used as the criterion, confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the Cressie-Read parameter {lambda}, including – 1, maximum entropy, 0, empirical likelihood, and 1, Pearson's {chi}2. It is noted that, in the power-divergence family, empirical likelihood is the only member which is Bartlettcorrectable. However, simulation results suggest that, for the mean, using a, scaled F distribution yields more accurate coverage levels for moderate sample sizes.

Key Words: Bartlett correction • Cressie-Read statistic • Empirical likelihood • Goodness-of-fit test • Maximum entropy • Nonparametric confidence region


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