广义平衡抽样及其模型辅助估计方法研究

The Study of Generalized Balanced Sampling and Its Model-assisted Estimation Method

当传统平衡抽样条件满足时,传统平衡抽样方法能够抽出代表性较强的样本,对应的Horvitz-Thompson估计量的估计效果也较好。但在实际抽样中,超总体模型为线性回归模型以及平衡变量的总体单元信息完全已知,这两个基本条件常常无法满足。因此,本文扩展了抽样设计阶段的传统平衡抽样条件,提出广义平衡抽样方法;改进了抽样估计阶段的传统平衡Horvitz-Thompson估计量,提出广义平衡回归估计量。该方法对超总体模型是否为线性模型以及平衡变量的总体单元信息是否已知没有限制,扩大了平衡抽样的适用范围。相比于传统平衡抽样,广义平衡抽样提高了平衡样本在总体中的代表性。同时,相比于传统估计量,广义平衡回归估计量的估计精度更高,方差更稳定,并且估计量具有渐近设计无偏性和一致性。数值模拟和实证分析结果均表明,当平衡变量与目标变量之间紧密相关时,广义平衡抽样及广义平衡回归估计量具有优越性。

When the conditions of traditional balanced sampling are satisfied,the traditional balanced sampling method can get the sample with strong representativeness,and the Horvitz-Thompson estimator is better under the balanced sample. However,in actual sampling,it is often impossible to satisfy the two basic conditions that the superpopulation model is a linear regression model and that the balanced variables are completely known for all units of the population. In the sampling design stage,this paper expands the traditional balanced sampling conditions and proposes a method of generalized balanced sampling. In the sampling estimation stage,this paper improves the traditional balanced Horvitz-Thompson estimator and proposes a generalized balanced regression estimator. This method has no limitation on whether the superpopulation model is linear or not and whether the population units of balanced variables are all known,and expands the scope of application of balanced sampling. Compared with traditional balanced sampling,the generalized balanced sampling improves the representativeness of balanced samples. Meanwhile,compared with the traditional estimator,the generalized balanced regression estimator has higher accuracy and more stable variance,and the estimator is asymptotically unbiased and consistent. The simulation and empirical analysis results show the superiority of the generalized balanced sampling and the generalized balanced regression estimator when there is a close correlation between the balance variable and the interest variable.