EMPIRICAL LIKELIHOOD IS BARTLETT-CORRECTABLE

被引:296
作者
DICICCIO, T [1 ]
HALL, P [1 ]
ROMANO, J [1 ]
机构
[1] AUSTRALIAN NATL UNIV,DEPT STAT,CANBERRA,ACT 2601,AUSTRALIA
关键词
BARTLETT CORRECTION; CHI-SQUARED APPROXIMATION; EMPIRICAL LIKELIHOOD RATIO STATISTIC; NONPARAMETRIC CONFIDENCE REGION; SIGNED ROOT EMPIRICAL LIKELIHOOD RATIO STATISTIC;
D O I
10.1214/aos/1176348137
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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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页码:1053 / 1061
页数:9
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