An empirical likelihood (EL) approach for a partial linear single-index model with censored response data is studied. A bias-corrected EL ratio is proposed, and the asymptotic chi-squared distribution of this ratio is obtained. The result can be directly used to construct the confidence regions of the regression parameters. The estimators of regression parameters and link function are constructed, and their asymptotic distributions are obtained. Also, a confidence band of the link function is constructed. The proposed method has two main features: The first feature is that the EL ratio is calibrated directly from within, instead of multiplying an adjustment factor by an EL ratio, which reflects the nature of EL. The second feature is avoiding undersmoothing of nonparametric functions, thus ensuring that the $\sqrt{n}$-consistency of the parameter estimator. As a byproduct, the EL and estimation of a single-index model with censored response data are studied. The performance of the bias-corrected EL is evaluated by the simulation studies. The proposed method is illustrated with an example of a real data analysis.

研究了带有删失响应数据的部分线性单指标模型的经验似然 (EL) 方法。提出了偏差校正的 EL 比率，并获得了该比率的渐近卡方分布。结果可以直接用于构建回归参数的置信区域。构造了回归参数和链接函数的估计量，并得到了它们的渐近分布。此外，还构建了链接函数的置信带。该方法有两个主要特点：第一个特点是直接从内部校准EL比率，而不是用EL比率乘以调整因子，这反映了EL的本质。第二个特征是避免非参数函数的欠平滑，从而确保$\sqrt{n}$-参数估计器的一致性。作为副产品，研究了带有删失响应数据的单指数模型的 EL 和估计。偏差校正 EL 的性能通过模拟研究进行评估。所提出的方法通过实际数据分析的例子进行说明。