EMPIRICAL LIKELIHOOD RATIO CONFIDENCE-INTERVALS FOR A SINGLE FUNCTIONAL
成果类型：
Article
署名作者：
OWEN, AB
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2336172
发表日期：
1988
页码：
237249
关键词：
摘要：
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.
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