Two-phase rejective sampling and its asymptotic properties
提出两阶段拒绝抽样方法，在第一阶段测量辅助变量，第二阶段对结果变量实施拒绝抽样，证明该方法能提升双扩展估计量的效率，并扩展至多阶段抽样和一般估计方程。
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. We start with the theory for the population mean and then extend the theory to parameters defined by general estimating equations. Our asymptotic results for TPRS immediately cover the existing single-phase rejective sampling, under which the asymptotic theory has not been fully established.