小样本空间制图

空间制图广泛运用于地学等领域。与单纯地对一个区域内的某个属性的全局均值估计不同，本研究着重考虑多报告单元（如行政区划或者人为划定的网格等），需要对每个报告单元的均值进行估计的情况。此时，为保证估值精度，抽样费用随报告单元增多而急剧增加；换言之，随着报告单元数增加，每个报告单元内的样本数相对减少，使得估计误差会增大。本研究致力于研发一种新的方法，运用方差分析结合"二次"分层统计解决多报告单元统计推断所面临的小样本问题。我们假设区域是异质的，即均值在整个区域内是变化的，且可以分层（stratified）为多个均质子区域，即每个子区域内的均值固定。各个分层单元内的统计信息传递到报告单元中。我们将通过一系列的理论推导和全国乙肝病毒携带率制图等实验，与其他已有方法的样本量和估值精度对比，以描述这种新方法的适用条件和实际应用效果。

Mapping is widely used in environmental and social research. In this proposal we consider the situation where instead of a single global estimate of the mean of an attribute for an area, estimates are required for each of many geographically defined reporting units (such as counties or grid cells) because their means cannot be assumed to be the same as the global figure. Not only may the cost of a survey greatly increase if sample size has to be a function of the number of reporting units, estimator sampling error tends to be large if the population attribute of each reporting unit can be estimated by using only those samples actually lying inside the unit itself. This study proposes a simple approach to multi-unit reporting by using analysis of variance (ANOVA) and incorporating 'twice' stratified statistics. We assume the area is heterogeneous (the mean varies across the area) but can be zoned (or stratified) into homogeneous sub-areas (the mean is constant within each sub area) and, in addition, that it is possible to acquire prior knowledge about this partition. This zoning of the study area is independent of the reporting units. The zone estimates are transferred to the reporting units. We will apply the new method to mapping HBsAg in China and other empirical studies, and to compare its performance against existing methods for tackling this problem.