Spatial Association Statistics

最近在空间分析和地理信息系统等相关方法方面取得的进展表明，需要更好地了解空间相关性和自相关性的统计特性。没有考虑空间自相关性可能会导致模型解释中的严重错误。空间建模不仅必须考虑相依结构和异方差，而且还必须评估空间尺度的影响。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，研究了一类新的空间关联统计量G。最终目标是将G统计数据纳入地理信息系统，以探讨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人使用了各种统计技术来衡量空间关联性。这一研究项目将为空间分布的分析增加一个更强大的工具，因为它直接应用于各种空间尺度。将G统计数据纳入地理信息系统将能够更严格地分析空间聚集的不同层面上的空间分布，从而将其用途扩展到许多不同的问题。

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.