The mean residual lifetime (MRL) of a unit in a population at a given time t, is the average remaining lifetime among those population units still alive at the time t. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained “free of charge”, at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show that the introduced technique can provide more accurate estimates for the average remaining lifetime of patients with breast cancer.

中文翻译：

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基于排序集抽样的递减平均剩余寿命估计并应用于生存分析

给定时间群体中某个单位的平均剩余寿命 (MRL)t，是当时还活着的人口单位的平均剩余寿命t。在某些应用中，可以合理地假设 MRL 函数是随时间递减的函数。因此，改进 MRL 函数估计的一种自然方法是在估计过程中使用这一假设。在本文中，我们在排序集采样（RSS）中开发了一种 MRL 估计器，它具有单调性。我们证明它是真实 MRL 函数的强一致一致估计器。我们还表明，引入的估计量的渐近分布与经验分布相同，因此新的估计量是“免费”获得的，至少在渐近意义上是这样。然后，我们使用蒙特卡罗模拟在 RSS 和简单随机抽样 (SRS) 方面将所提出的估计器与其竞争对手进行比较。我们的模拟结果证实了所提出的程序对于有限样本量的优越性。最后，使用美国国家癌症研究所（NCI）监测、流行病学和最终结果（SEER）项目的真实数据集表明，所引入的技术可以为乳腺癌患者的平均剩余寿命提供更准确的估计。