In this paper, we define estimators of distribution functions when the data are right-censored and the censoring indicators are missing at random, and establish their strong representations and asymptotic normality. Besides, based on empirical likelihood method, we define maximum empirical likelihood estimators and smoothed log-empirical likelihood ratios of two-sample quantile difference in the presence and absence of auxiliary information, respectively, and prove their asymptotic distributions. Simulation study and real data analysis are conducted to investigate the finite sample behavior of the proposed methods.

中文翻译：

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审查指标随机缺失的分位数差异估计

在本文中，我们定义了数据右删失且删失指标随机缺失时的分布函数估计量，并建立了它们的强表示和渐近正态性。此外，基于经验似然法，我们分别定义了存在辅助信息和不存在辅助信息的情况下的最大经验似然估计和两样本分位数差的平滑对数经验似然比，并证明了它们的渐近分布。进行仿真研究和实际数据分析来研究所提出方法的有限样本行为。