有序信息在空间立方体抽样中的拓展研究

Extension of Ordered Information in Spatial Cube Sampling

在空间调查领域中,分布良好的样本中很少会同时出现彼此接近的单元.将地理坐标作为平衡变量的立方体法存在无法捕捉总体单元的空间依赖性的不足.文章在立方体法能有效捕获总体空间趋势的基础上,创新性地引入系统抽样的思想.文章提出的抽样设计方法在保持单元空间相对位置的同时,充分利用地理坐标信息,集中相似单元点获得有序总体,使原先总体具有“空间趋势”.首先,在保持空间相关性的前提下,将抽样单元排序问题转换为单源最短路径问题.然后,利用Dijkstra算法获得有序总体,在快速立方体法的飞行阶段更新初始包含概率进行有序空间抽样.最后,通过模拟研究和实证分析表明对空间总体按照相似单元彼此靠近的原则进行排序,可减少抽样误差,获得较为均衡的样本,从而验证所提抽样思路的可行性.

In the field of spatial investigation,it is rare for a well-distributed sample to have units close to each other at the same time.The cube method using geographic coordinates as the equilibrium variable has the shortcoming of not capturing the spatial dependence of the total unit.In this paper,the idea of systematic sampling is innovatively introduced on the basis that cube method can capture the overall spatial trend effectively.The sampling design method proposed in this paper makes full use of the geographic coordinate information while keeping the relative position of the unit space,and gathers similar unit points to obtain the ordered population,so that the original population has a“spatial trend”.First,the sampling unit ordering problem is transformed into a single source shortest path problem while maintaining the spatial correlation.Then,Dijkstra algorithm is used to obtain the ordered population,and the initial inclusion probability is updated in the flight phase of the fast cube method for ordered space sampling.Finally,through the simulation study and empirical analysis,it is shown that sorting the spatial population according to the principle of similar units being close to each other can reduce the sampling error and obtain a more balanced sample,so as to verify the feasibility of the proposed sampling idea.