Ordered ranked set sample and applications to statistical inference

具有成本效益的抽样方法是统计学上主要关注的问题。排序集抽样(RSS)最早于1952年提出。在被遗忘了很长一段时间后，RSS的价值在最近几年重新被发现，因为它的性价比。现在，RSS方法在农业、林业、生态科学、环境科学甚至医学研究等领域都引起了人们的实际兴趣。直到最近，有关排序集抽样的文献和研究都是基于排序集样本本身或排序集样本的顺序统计量的渐近性质。但在一些实际问题中，除了RSS本身之外，还需要RSS(ORSS)的顺序统计量。在过去的几年里，我们成功地导出了ORSS的分布，并将其应用于一些统计推断。这项建议的一部分是保持势头，并探索ORSS在统计推理中的更多应用。此外，我们将我们的工作推广到不完全排序，这更适合于实际问题。

Cost-effective sampling methods are of major concern in statistics. Ranked set sampling (RSS) was first proposed in 1952. After being forgotten for quite a while, the value of RSS was rediscovered in recent years because of its cost-effective nature. Now, RSS method attracts practical interest in areas such as agriculture, forestry, ecological science, environmental science, and even medical studies. Until recently, the publications and research about ranked set sampling are based on ranked set sample itself or on asymptotical properties of order statistics of ranked set sample. But in some practical problems, the order statistics of RSS (ORSS) other than the RSS itself are desired. In the past few years, we successfully derived the distribution of ORSS, and applied it to somce statistical inferences. Part of this proposal is to keep the momentum and to explore more applications of ORSS to statistical inference. Moreover, we will generalize our work to imperfect ranking, which is more suitable for practical problems.