EMPIRICAL LIKELIHOOD AND GENERAL ESTIMATING EQUATIONS
EMPIRICAL LIKELIHOOD AND GENERAL ESTIMATING EQUATIONS
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DOI：
10.1214/aos/1176325370
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发表时间：
1994-03-01
影响因子：
4.5
通讯作者：
LAWLESS, J
中科院分区：
文献类型：
--
作者：
QIN, J;LAWLESS, J
一段时间以来，所谓的经验可能性一直用于非参数估计的目的。欧文（Owen）表明，未知分布f的各种参数（f）的经验可能性比统计量具有限制性卡方分布，可用于以完全类似于参数类似物的方式获得测试或置信区间。本文我们的目标是双重的：首先，链接估计功能或方程式以及经验可能性；其次，开发结合有关参数信息的方法。我们通过假设有关F和Theta的信息以无偏估计功能的形式获得。开发了参数的经验可能性，并显示出与参数可能性相似的属性。获得了theta和f的估计值的效率结果。这些方法在几个问题上进行了说明，并注意到未来研究的领域。
For some time, so-called empirical likelihoods have been used heuristically for purposes of nonparametric estimation. Owen showed that empirical likelihood ratio statistics for various parameters theta(F) of an unknown distribution F have limiting chi-square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parameteric likelihoods. Our objective in this paper is twofold: first, to link estimating functions or equations and empirical likelihood; second, to develop methods of combining information about parameters. We do this by assuming that information about F and theta is available in the form of unbiased estimating functions. Empirical likelihoods for parameters are developed and shown to have properties similar to those for parameteric likelihood. Efficiency results for estimates of both theta and F are obtained. The methods are illustrated on several problems, and areas for future investigation are noted.