EMPIRICAL LIKELIHOOD IS BARTLETT-CORRECTABLE
EMPIRICAL LIKELIHOOD IS BARTLETT-CORRECTABLE
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DOI：
10.1214/aos/1176348137
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发表时间：
1991-06-01
影响因子：
4.5
通讯作者：
ROMANO, J
中科院分区：
文献类型：
--
作者：
DICICCIO, T;HALL, P;ROMANO, J
研究表明，在非常一般的情形下，用于构建置信区间的经验似然方法是可进行巴特利特校正的。这意味着对对数似然比的期望值进行简单调整，可将覆盖误差降低到极低的\(O(n^{-2})\)，其中\(n\)表示样本量。这一事实使得经验似然与诸如自助法等方法具有竞争力，自助法是不可进行巴特利特校正的，并且通常具有\(n^{-1}\)量级的覆盖误差。最重要的是，我们的工作表明了经验似然与参数似然之间的紧密联系，因为巴特利特校正此前仅适用于参数似然。给出了一个适用于非常广泛问题的巴特利特校正的通用公式，包括均值、方差、协方差、相关性、偏度、峰度、均值比、均值差、方差比等的估计。通过对均值情况的模拟研究证明了该校正的有效性。
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.