In this article, we construct empirical likelihood (EL)-weighted estimators of linear functionals of a probability measure in the presence of side information. Motivated by nuisance parameters in semiparametric models with possibly infinite dimensions, we consider the use of estimated constraint functions and allow the number of constraints to grow with the sample size. We study the asymptotic properties and efficiency gains. The results are used to construct improved estimators of parameters in structural equation models. The EL-weighted estimators of parameters are shown to have reduced variances in a SEM in the presence of side information of stochastic independence of the random error and random covariate. Some simulation results on efficiency gain are reported.

翻译：在本篇文章中,我们用附带信息来计算概率计量线性功能的经验概率(EL)加权估计值。受可能具有无限尺寸的半对数模型中的干扰参数的驱使,我们考虑使用估计约束功能,并允许随着抽样规模的增加而增加限制数量。我们研究无症状特性和效率收益。结果用于在结构等式模型中建立改进的参数估计值。EL加权参数估计值显示,在存在随机差错和随机共变的侧端信息的情况下,欧经会议差异减少。报告了一些关于效率收益的模拟结果。