Long range dependence and resampling methodology for spatial data

该项目致力于(I)在各种空间抽样设计下发展一类长程相关空间过程的极限理论，包括空间应用中经常遇到的不规则间隔数据站点的情况；(Ii)发展新的不受维度诅咒影响的短程和长程相关空间数据的重采样方法；(Iii)发展规则和不规则间隔情况下空间数据的Edgeworth展开理论；以及(Iv)研究空间数据重采样方法的高阶性质并研究其高阶性质。拟议的项目旨在对空间统计的几个关键领域作出重要的理论和方法贡献，这些领域具有广泛的潜在应用，但目前关于这些领域的文献很少。除了改进空间参照数据的统计方法状况外，拟议的研究还将有益于许多其他科学领域，如天文学、水文学、地质学、经济学、大气科学等，在这些领域，空间数据表现出不同形式的依赖关系是自然发生的，而项目中提出的那些无模型统计方法在这些领域的分析中发挥着重要作用。此外，该项目将通过指导博士生和指导初级研究人员来开发人力资源。

This project concentrates on (i) developing limit theory for a class of long range dependent spa­tial processes under various spatial sampling designs, including the case of irreguraly spaced data-sites, which is encountered frequently in spatial applications; (ii) developing new resampling methodology for spatial data under both short-and long-range dependence that are immune to the e.ects of the curse of dimensionality, (iii) developing Edgeworth expansion theory for spatial data for both regularly and irregularly spaced cases, and (iv) investigating higher order properties of resampling methods for spatial data and study their higher order properties. The proposed project aims to make important theoretical and methodological contributions to several critical areas of spatial statistics that have a wide of potential applications but the state of the current literature on these areas is very sparse. In addition to advancing the state of statistical methodology for spatially referenced data, the proposed research would also bene.t many other areas of sciences, such as Astronomy, Hydrology, Geology, Economics, Atmospheric Sciences, etc. where spatial data exhibiting di.erent forms of dependence are known to occur naturally, and model-free statistical methods such as those proposed in the project play an important role in their analysis. Further, the project would lead to the development of human resources through advising of Ph.D. students and mentoring of junior researchers.