地理空间中不同分层抽样方式的分层效率与优化策略

地理空间对象中分层抽样的效率受抽样总体的空间相关性特征限制,分层效率的提高源于两个方面,一是 抽样总体的空间相关性会使分散的样本布局精度得到提高,二是先验知识使层内方差变小,只有在空间相关性特 征较强时,追逐先验知识的分层方式才会比任意分层方式具有更好的分层效率,当空间相关性较弱时,知识分层并 不会比任意分层得到更高的抽样精度,地理空间相关性特征对分层抽样设计有重要影响,而这在实际应用中往往 被忽视。本文采用蒙特卡罗模拟抽样方法以山东省1985 年和1995 年细小非耕地地物面积比例的抽样调查为例分 析了空间相关性特征对不同分层方式抽样效率的影响,并提出了地理空间对象中分层方式的优化选择策略。

Str ata Efficiency and Optimization str ategy of Str atified Sampling on Spatial Population

Efficiency of stratified sampling for geospatial population is restricted by spatial auto-correlation. Strata efficiency origins from two aspects: the first is spatial auto-correlation, which makes sampling with dispersed distribution improve the accuracy; and the second is priori knowledge, which can make the variance smaller within strata than within the overall population. The strata efficiency for knowledge strata is more outstanding than that of arbitrary strata only in the geographical object with strong spatial auto-correlation; when the spatial auto-correlation is weak, knowledge will not be preferred to the arbitrary strata. Spatial auto-correlation has an important influence on stratified sampling design: Although a stratified statostoc always "gains" in terms of accuracy, the implementation of the technique is conditional, expensive and sometime unnecessary. This is often overlooked in practical application. Different stratified sampling surveys for the ratio of thin-non-cultivated component in Shandong Province are simulated by using Mento Carlo method. Simulated results validate the influence of spatial: auto-correlation on different stratified methods. Finally, this paper proposes optimization strategy of strata selection for geospatial objects.