分层抽烟设计中层界确定方法的比较研究.pdf

摘 要 抽样调查方法伴随着经济的发展已经深入到社会生活的各个领域，而作为 抽样调查中最为重要的调查技术——分层抽样方法几乎成为所有调查中必备的 方法之一。由于它能够将数据按照“层间差异大，层内差异小”的原则进行化 分，从而大大提高估计量的精度，因此分层抽样技术越来越得到广泛的重视和 有关专家学者的宠爱。 但是，分层抽样方法并不是完美无缺的。在分层优化设计理论中，分层抽 样设计应包括“层数定多少、样本量在各层如何分配、各层的层界如何确定” 这三个部分，设计的总目标和总原则自然是既定样本量下抽样精度最高（在不 考虑费用函数情况下），但是各层层界如何确定在该原则下至今仍没有完美的答 案。 本文主要针对分层抽样设计中“各层层界如何确定”为主题展开分析讨论， 通过模拟和实证分析分别比较“累计平方根方法”和“几何分布方法”在层界 确定方式上的优劣。模拟比较分析结论为：在对研究变量分层设计时，从总体 分布的不同形状入手得到累计平方根法的效率要明显好于几何分布法。同时， 在用辅助变量分层时，针对辅助变量不同的相关程度，表明了累计平方根法的 分层效果更优；在实证比较分析方面，主要针对国家外汇贸易信贷数据进行讨 论，结果证明：出口数据中累计平方根法更有效率，而进口数据二者效率几乎 无明显差异，综合来看，累计平方根法更适用于全国贸易信贷调查。 关键词：分层抽样；层界；抽样精度；累计平方根法；几何分布法 1 Abstract Sample survey methods associated with economic development has been deep into all areas of social life. As a sample survey of the most important investigative techniques, the stratified sampling method has become the most necessary methods in almost all investigations. As the data could be stratified in accordance with the principle of large difference between layers and small difference in layer, so the accuracy of the study variables estimation is far higher than other sampling methods, that is why it is so popular for the relevant experts and scholars. However, the stratified sampling method is not perfect. In the hierarchical theory of optimal design, stratified sampling design should include fixed number of layers, the distribution of sample size in the layers, how to determine the layer industry. The designs overall goals and general principles is to get the highest precision under the fixed sample size (without regard to the cost function), but there is still no perfect answer about how to identify