Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS.

中文翻译：

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最优抽样设计下使用辅助信息对人口均值的比率估计

在某些实验中，成本效益的抽样设计是一个主要关注的问题，特别是当感兴趣特征的测量成本高昂或痛苦或耗时时。在本文中，我们使用排序集抽样 (RSS) 和极端排序集抽样 (ERSS) 方案研究了研究变量总体均值的比率型估计量，涉及辅助变量的第一或第三四分位数。获得了估计量的性质。RSS 和 ERSS 中的估计量与普通数据的简单随机抽样 (SRS) 中的估计量进行比较。数值结果表明，RSS 和 ERSS 中的估计器明显比 SRS 中的估计器更有效。