For many clustered populations, the prior information on an initial stratification exists but the exact pattern of the population concentration may not be predicted. Under this situation, the stratified adaptive cluster sampling (SACS) may provide more efficient estimates than the other conventional sampling designs for the estimation of rare and clustered population parameters. For practical interest, we propose a generalized ratio estimator with the single auxiliary variable under the SACS design. The expressions of approximate bias and mean squared error (MSE) for the proposed estimator are derived. Numerical studies are carried out to compare the performances of the proposed generalized estimator over the usual mean and combined ratio estimators under the conventional stratified random sampling (StRS) using a real population of redwood trees in California and generating an artificial population by the Poisson cluster process. Simulation results show that the proposed class of estimators may provide more efficient results than the other estimators considered in this article for the estimation of highly clumped population.

中文翻译：

---

使用分层自适应聚类抽样估计稀有和聚类总体均值

对于许多聚集人口，存在有关初始分层的先验信息，但可能无法预测人口集中的确切模式。在这种情况下，分层自适应聚类采样（SACS）可以比其他常规采样设计提供更有效的估计，以估计稀有和聚集的种群参数。出于实际利益，我们建议在SACS设计下使用单个辅助变量的广义比率估计器。近似偏差和均方误差（MSE）得出建议的估算器。进行了数值研究，以比较使用加利福尼亚州的红木真实种群并通过泊松聚类过程生成人工种群的情况下，在常规分层随机抽样（StRS）下，所提出的广义估计与常规均值和组合比率估计的性能。仿真结果表明，所提出的估计量类别可能比本文中考虑的其他估计量提供更有效的结果，用于估计高度聚集的总体。