关键词: 平衡变量, 超总体模型, 广义平衡抽样, 模型辅助估计, 广义平衡回归估计

Abstract: 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.

Key words: Balanced Variable, Superpopulation Model, Generalized Balanced Sampling, Model-assisted Estimation, Generalized Balanced Regression Estimation