## The Annals of Statistics

### Empirical Likelihood is Bartlett-Correctable

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 19, Number 2 (1991), 1053-1061.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176348137

Digital Object Identifier
doi:10.1214/aos/1176348137

Mathematical Reviews number (MathSciNet)
MR1105861

Zentralblatt MATH identifier
0725.62042

JSTOR