Rejective sampling improves design and estimation efficiency of single-phase sampling when auxiliary information in a finite population is available. When such auxiliary information is unavailable, we propose to use two-phase rejective sampling (TPRS), which involves measuring auxiliary variables for the sample of units in the first phase, followed by the implementation of rejective sampling for the outcome in the second phase. We explore the asymptotic design properties of double expansion and regression estimators under TPRS. We show that TPRS enhances the efficiency of the double expansion estimator, rendering it comparable to a regression estimator. We further refine the design to accommodate varying importance of covariates and extend it to multi-phase sampling.

翻译：拒绝抽样在有限总体中可利用辅助信息时，能提升单阶段抽样的设计与估计效率。当此类辅助信息不可获得时，我们提出采用两阶段拒绝抽样（TPRS），该方法在第一阶段对抽样单元测量辅助变量，随后在第二阶段对结果变量实施拒绝抽样。我们探究了TPRS下双重扩展估计量与回归估计量的渐近设计性质。研究表明，TPRS能够提升双重扩展估计量的效率，使其达到与回归估计量相近的水平。我们进一步对设计进行优化以适配协变量的不同重要性，并将其拓展至多阶段抽样场景。