Spatial Association Statistics

空间分析和地理信息系统等相关方法的最新进展表明，需要更好地了解空间相关和自相关的统计特性。不考虑空间自相关会导致模型解释出现严重错误。空间建模不仅要考虑依赖结构和异方差，而且要考虑空间尺度的影响。本文通过对空间分布变量在不同情况下，特别是在小样本情况下的实验，重点研究了一种新的空间关联统计量G。最终目的是将G统计量纳入地理信息系统，以探索空间依赖性和空间异质性对各种分析模型的影响。地理学家、地质学家和计量经济学家等已经使用了各种统计技术来测量空间关联。该研究项目可直接应用于各种空间尺度，为空间分布分析提供了更有力的工具。将G统计数据集成到地理信息系统中，将允许对不同空间聚集水平的空间分布进行更严格的分析，从而将其应用于许多不同的问题。

Recent advances in spatial analysis and related methodologies such as geographical information systems have pointed up the need for a better understanding of the statistical properties of spatial correlation and autocorrelation. Failure to take spatial autocorrelation into account can lead to serious errors in model interpretation. Spatial modeling must not only take account of dependence structure and heteroscedasticity, but it must also assess the effects of spatial scale. This research focuses on a new family of spatial association statistics, G, by experimentation on spatially distributed variables in different situations, especially with small samples. The ultimate objective is to incorporate the G statistics into geographical information systems in order to explore the influence of spatial dependence and spatial heterogeneity on a variety of analytical models. Geographers, geologists and econometricians, among others, have used a variety of statistical techniques for measuring spatial association. This research project will add a more powerful tool for the analysis of spatial distributions, because of its direct application at a variety of spatial scales. Integration of the G statistics into geographical information systems will permit more rigorous analysis of spatial distributions at different levels of spatial aggregation, thus extending their utility to many different problems.