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June, 1991 Empirical Likelihood is Bartlett-Correctable
Thomas DiCiccio, Peter Hall, Joseph Romano
Ann. Statist. 19(2): 1053-1061 (June, 1991). DOI: 10.1214/aos/1176348137


It is shown that, in a very general setting, the empirical likelihood method for constructing confidence intervals is Bartlett-correctable. This means that a simple adjustment for the expected value of log-likelihood ratio reduces coverage error to an extremely low $O(n^{-2})$, where $n$ denotes sample size. That fact makes empirical likelihood competitive with methods such as the bootstrap which are not Bartlett-correctable and which usually have coverage error of size $n^{-1}$. Most importantly, our work demonstrates a strong link between empirical likelihood and parametric likelihood, since the Bartlett correction had previously only been available for parametric likelihood. A general formula is given for the Bartlett correction, valid in a very wide range of problems, including estimation of mean, variance, covariance, correlation, skewness, kurtosis, mean ratio, mean difference, variance ratio, etc. The efficacy of the correction is demonstrated in a simulation study for the case of the mean.


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Thomas DiCiccio. Peter Hall. Joseph Romano. "Empirical Likelihood is Bartlett-Correctable." Ann. Statist. 19 (2) 1053 - 1061, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62042
MathSciNet: MR1105861
Digital Object Identifier: 10.1214/aos/1176348137

Primary: 62A10
Secondary: 62G05

Keywords: Bartlett correction , chi-squared approximation , empirical likelihood ratio statistic , nonparametric confidence region , signed root empirical likelihood ratio statistic

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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