复杂抽样推断方法体系的比较研究

A Comparative Study of Complex Sampling Inference Systems

对复杂样本进行推断通常有两种体系,一种是传统的基于随机化理论的统计推断,另一种是基于模型的统计推断。传统的抽样理论以随机化理论为基础,将总体取值视为固定,随机性仅体现在样本的选取上,对总体的推断依赖于抽样设计。该方法在大样本情况下具有稳健估计量,但在小样本、数据缺失等情况下失效。基于模型的抽样推断认为总体是超总体模型中抽取的一个随机样本,对总体的推断取决于模型的建立,但在不可忽略抽样设计下估计量是有偏估计。在对这两类推断方法分析的基础上,提出抽样设计辅助的模型推断,并指出该方法在复杂抽样中具有重要的应用价值。

There are usually two inference systems for complex sample： traditional statistical inference and model-based statistical inference. Traditional sampling theory based on randomization theory believed that the values of variables on population units are fixed and the randomness embodies in sample selection. Its inference for population depends on sampling design. Estimators of this method are robust when sample size is large, but inefficiency when sample size is small and there are missing data. Another deduction based on model thinks that the finite population is a random sample drawn from a super-population. Inference for population depends on modeling, but estimators of this inference system are biased under non -ignorable sample scheme. Based on the analysis of the core contents of the two methods, this paper proposes sampling scheme-assisted and model-based inference, and points out that this method has important application value in complex sampling.