On Profile Likelihood
本文证明半参数剖面似然具有与普通似然类似的二次展开，其中得分函数和Fisher信息被有效得分函数和有效Fisher信息替代，可用于证明最大似然估计的渐近正态性、似然比统计量的渐近卡方分布等。
Abstract 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.