ABSTRACT The mean residual life (MRL) function for a given random variable T is the expected remaining lifetime of T after a fixed time point t. It is of great interest in survival analysis, reliability, actuarial applications, duration modelling, etc. Liang, Shen, and He [‘Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable’, Acta Mathematicae Applicatae Sinica, English Series, 32, 269–282] proposed empirical likelihood (EL) confidence intervals for the MRL based on length-biased right-censored data. However, their -2log(EL ratio) has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose a new empirical likelihood (NEL) based on i.i.d. representation of Kaplan–Meier weights involved in the estimating equation. We also develop the adjusted new empirical likelihood (ANEL) to improve the coverage probability for small samples. The performance of the NEL and the ANEL compared to the existing EL is demonstrated via simulations: the NEL-based and ANEL-based confidence intervals have better coverage accuracy than the EL-based confidence intervals. Finally, our methods are illustrated with a real data set.

中文翻译：

---

具有长度偏向和右删失数据的平均剩余寿命的新经验似然推断

摘要 给定随机变量 T 的平均剩余寿命 (MRL) 函数是在固定时间点 t 之后 T 的预期剩余寿命。对生存分析、可靠性、精算应用、持续时间建模等非常感兴趣。 Liang, Shen, and He ['Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable', Acta Mathematicae Applicatae Sinica, English Series, 32, 269–282] 基于长度偏向右删失数据提出了 MRL 的经验似然 (EL) 置信区间。然而，它们的 -2log(EL ratio) 具有缩放的卡方分布。为了避免在构建置信区间时估计尺度参数，我们基于估计方程中涉及的 Kaplan-Meier 权重的 iid 表示提出了一种新的经验似然 (NEL)。我们还开发了调整后的新经验似然 (ANEL) 以提高小样本的覆盖概率。NEL 和 ANEL 与现有 EL 相比的性能通过模拟得到证明：基于 NEL 和基于 ANEL 的置信区间比基于 EL 的置信区间具有更好的覆盖精度。最后，我们的方法用一个真实的数据集来说明。