In this paper, we focus on the empirical likelihood inference for partially linear single-index errors-in-variables (EV) models when the data are right censored and the censoring indicator is missing at random (MAR). Two bias-corrected empirical log-likelihood ratio (BCELR) functions for the parameters by using regressing calibration and imputation methods are introduced. The limiting distributions of the BCELRs are shown to have a mixture of central chi-squared distribution. Based on this, the confidence regions of the parameters can be constructed by using bootstrap approximation. Furthermore, as there would be some spurious covariates in the linear and nonlinear parts, a penalized empirical likelihood (PEL) approach is proposed with the help of smoothly clipped absolute deviation penalty. Two proposed PEL estimators are shown to possess the oracle property. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of the proposed methods.

在本文中，当数据被正确删失且删失检查指标随机（MAR）时，我们着重研究部分线性单指标变量误差（EV）模型的经验似然推断。介绍了两种回归校正的经验对数似然比（BCELR）函数，分别采用回归标定和插补方法。显示BCELR的极限分布具有中心卡方分布的混合。基于此，可以通过使用自举近似来构造参数的置信区域。此外，由于线性和非线性部分中会存在一些虚假的协变量，因此在平滑限幅绝对偏差惩罚的帮助下，提出了一种惩罚性经验似然（PEL）方法。显示了两个建议的PEL估计器具有oracle属性。进行了仿真研究和真实数据分析，以评估所提出方法的有限样本性能。