This project concentrates on (i) developing limit theory for a class of long range dependent spaÂtial 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.
