In this paper, we propose a presmooth product-limit estimator to draw statistical inference on the unbiased distribution function representing the population of interest. The strong consistency of the estimator proposed is investigated. The finite sample performance of the proposed estimator is evaluated using simulation studies. It is observed that the proposed estimator exhibits greater efficiency in comparison with the alternative method in de Uña-Álvarez (Test 11(1):109–125, 2002).

中文翻译：

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带有长度偏向数据的无偏分布的平滑估计

在本文中，我们提出了一个平稳的乘积极限估计量，以对代表目标人群的无偏分布函数进行统计推断。研究了估计量的强一致性。拟议估计量的有限样本性能通过仿真研究进行评估。可以看出，与deUña-Álvarez中的替代方法相比，拟议的估计量具有更高的效率（Test 11（1）：109-125，2002）。