On profile likelihood
On profile likelihood
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DOI：
10.2307/2669386
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发表时间：
2000-06-01
影响因子：
3.7
通讯作者：
Van der Vaart, AW
中科院分区：
文献类型：
--
作者：
Murphy, SA;Van der Vaart, AW
我们证明了半参数轮廓似然，其中干扰参数已经轮廓化，表现得像普通的似然，因为它们有二次展开。在这个扩展中，分数函数和Fisher信息被替换为有效分数函数和有效Fisher信息。该展开式可用于证明极大似然估计量的渐近正态性，导出对数似然比统计量的渐近卡方分布，并证明观测信息作为渐近方差逆的估计量的一致性。
We show that semiparametric profile likelihoods, where the nuisance parameter has been profiled out, behave like ordinary likelihoods in that they have a quadratic expansion. In this expansion the score function and the Fisher information are replaced by-the efficient score function and efficient Fisher information. The expansion may be used, among others, to prove the asymptotic normality of the maximum likelihood estimator, to derive the asymptotic chi-squared distribution of the log-likelihood ratio statistic, and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance.