Long range dependence and resampling methodology for spatial data

该项目集中于(i)在各种空间采样设计下，为一类长距离依赖的空间过程发展极限理论，包括在空间应用中经常遇到的不规则间隔数据点的情况；（ii）为不受维数诅咒影响的短期和长期依赖的空间数据开发新的重采样方法；（iii）为规则和不规则间隔情况下的空间数据开发Edgeworth展开理论；（iv）调查空间数据重采样方法的高阶性质并研究其高阶性质。拟议的项目旨在为空间统计的几个关键领域做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非常稀少。除了促进空间参考数据的统计方法的现状外，拟议的研究也将受益。在许多其他科学领域，如天文学、水文学、地质学、经济学、大气科学等，空间数据表现出di。事件形式的依赖性是自然发生的，无模型统计方法（如项目中提出的那些）在它们的分析中起着重要的作用。此外，该项目将通过为博士生提供建议和指导初级研究人员来促进人力资源的发展。

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.