In agricultural and environmental surveys, obtaining spatially balanced area samples that are also representative probability samples in the presence of auxiliary variables is a challenge, especially when the study regions have fragmentary boundaries and possess holes of various shapes. This paper describes a sampling procedure that achieves this goal and is implemented in the U.S. Department of the Interior Bureau of Land Management (BLM) Rangeland Survey, a longitudinal environmental survey. This survey aims to assess status and trends of rangeland conditions on BLM-managed lands. In the sampling procedure, we first generate a 10-year master sample using Thiessen polygons and then draw annual samples through rejective sampling techniques using elevation as the auxiliary variable. The resulting annual samples as well as any consecutive multi-year combined samples are spatially well-dispersed and representative probability samples. Details about the sampling design, weighting procedure and replicate variance estimation are provided. Issues related to boundary error, ineligibility and nonresponse are also discussed. Some of the empirical results from the BLM Rangeland Survey are presented. Supplementary materials accompanying this paper appear online.

中文翻译：

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为土地管理局牧场调查局获取平衡面积样本

在农业和环境调查中，在存在辅助变量的情况下获得空间平衡的区域样本也是一个具有代表性的概率样本是一个挑战，特别是当研究区域的边界不完整并且具有各种形状的孔洞时。本文描述了实现这一目标的抽样程序，并在美国内政部土地管理局 (BLM) 牧场调查（一项纵向环境调查）中实施。该调查旨在评估 BLM 管理的土地上牧场条件的现状和趋势。在抽样过程中，我们首先使用泰森多边形生成一个 10 年的主样本，然后使用高程作为辅助变量通过拒绝抽样技术抽取年度样本。由此产生的年度样本以及任何连续的多年合并样本是空间分散良好且具有代表性的概率样本。提供了有关抽样设计、加权程序和重复方差估计的详细信息。还讨论了与边界错误、不合格和不答复有关的问题。介绍了 BLM 牧场调查的一些实证结果。本文随附的补充材料出现在网上。