EMPIRICAL LIKELIHOOD RATIO CONFIDENCE-INTERVALS FOR A SINGLE FUNCTIONAL
EMPIRICAL LIKELIHOOD RATIO CONFIDENCE-INTERVALS FOR A SINGLE FUNCTIONAL
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DOI：
10.1093/biomet/75.2.237
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发表时间：
1988-06-01
期刊：
影响因子：
2.7
通讯作者：
OWEN, AB
中科院分区：
文献类型：
--
作者：
OWEN, AB
基于样本的经验分布函数是众所周知的，是从其中提取样本的分布的最大似然估计。本文利用分布的似然函数定义了分布的似然比函数。结果表明，这种经验似然比函数可以用来构造置信区间的样本均值，一类M-估计，包括分位数，和可微的统计泛函。结果是威尔克斯（1938）参数似然比定理的非参数扩展。在一些真实的数据上说明了这些区间，并在模拟中与一些Bootstrap置信区间和基于Student's t统计量的区间进行了比较。介绍了一种利用自举法确定似然比临界值的混合方法。
The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable statistical functionals. The results are nonparametric extensions of Wilks''s (1938) theorem for parametric likelihood ratios. The intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on Student''s t statistic. A hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced.