If the population is rare and clustered, then simple random sampling gives a poor estimate of the population total. For such type of populations, adaptive cluster sampling is useful. But it loses control on the final sample size. Hence, the cost of sampling increases substantially. To overcome this problem, the surveyors often use auxiliary information which is easy to obtain and inexpensive. An attempt is made through the auxiliary information to control the final sample size. In this article, we have proposed two-stage negative adaptive cluster sampling design. It is a new design, which is a combination of two-stage sampling and negative adaptive cluster sampling designs. In this design, we consider an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known. In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, using Thompson’s (J Am Stat Assoc 85:1050–1059, 1990) adaptive procedure networks in the population are discovered. These networks serve as the primary-stage units (PSUs). In the second stage, random samples of unequal sizes are drawn from the PSUs to get the secondary-stage units (SSUs). The values of the auxiliary variable and the variable of interest are recorded for these SSUs. Regression estimator is proposed to estimate the population total of the variable of interest. A new estimator, Composite Horwitz–Thompson (CHT)-type estimator, is also proposed. It is based on only the information on the variable of interest. Variances of the above two estimators along with their unbiased estimators are derived. Using this proposed methodology, sample survey was conducted at Western Ghat of Maharashtra, India. The comparison of the performance of these estimators and methodology is presented and compared with other existing methods. The cost–benefit analysis is given.

中文翻译：

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两阶段负自适应聚类采样

如果人口稀少且聚集，那么简单的随机抽样将无法很好地估计人口总数。对于此类人群，自适应聚类采样很有用。但是它失去了对最终样本大小的控制。因此，采样成本大大增加。为了克服这个问题，测量师经常使用容易获得且廉价的辅助信息。试图通过辅助信息来控制最终样本量。在本文中，我们提出了两阶段负自适应群集抽样设计。这是一个新设计，是两阶段采样和负自适应群集采样设计的组合。在此设计中，我们认为辅助变量与关注变量高度负相关，并且辅助信息是完全已知的。在设计的第一阶段，使用辅助信息绘制初始随机样本。此外，使用汤普森（Thompson's（J Am Stat Assoc 85：1050-1059，1990））发现了人群中的适应性程序网络。这些网络用作主要阶段单元（PSU）。在第二阶段，从PSU中抽取大小不等的随机样本，以获得二级单位（SSU）。记录这些SSU的辅助变量和目标变量的值。建议使用回归估计器来估计感兴趣变量的总体。还提出了一种新的估计器，即复合Horwitz-Thompson（CHT）型估计器。它仅基于有关目标变量的信息。推导了以上两个估计量的方差以及它们的无偏估计量。使用这种提议的方法，在印度马哈拉施特拉邦的西高止山脉进行了抽样调查。给出了这些估计器和方法的性能比较，并与其他现有方法进行了比较。进行了成本效益分析。