Long range dependence and resampling methodology for spatial data

本项目的主要内容是：（1）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，包括在空间应用中经常遇到的数据点间距不规则的情况; ㈡为不受维数灾难影响的短期和长期依赖的空间数据开发新的检索方法，（iii）发展空间数据的Edgeworth展开理论，包括规则和不规则空间数据的Edgeworth展开理论;（iv）研究空间数据的重采样方法的高阶性质，并研究它们的高阶性质。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非常稀少。除了推进空间参考数据的统计方法的状态，拟议的研究也将贝内许多其他科学领域，如天文学，水文学，地质学，经济学，大气科学等，其中空间数据表现出不同形式的依赖性是已知的自然发生，和无模型的统计方法，如在项目中提出的那些在其分析中发挥重要作用。此外，该项目还将通过博士生的咨询促进人力资源的开发。学生和指导初级研究人员。

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.