Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless (1994) remains an active research topic. When the response is missing at random (MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation (AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.

Qin和Lawless（1994）的一般估计方程定义的参数的基于经验似然性推断仍然是一个活跃的研究主题。当响应随机缺失（MAR）且协变量的维数不低时，作者提出了一个两阶段的估计程序，该方法将维数减少的核估计器与基于增强的逆概率加权的无偏估计函数结合使用。多重插补（AIPW-MI）方法。作者表明，所得的估计量达到了一致性和渐近正态性。另外，当在真实参数下评估时，相应的经验似然比统计量渐近地遵循中心卡方分布。通过仿真研究了所提出估计量的有限样本性能，