Resampling methods for temporal and spatial processes and their higher order accuracy

该项目侧重于研究时间序列和空间数据的常见重采样方法的高阶渐近性质，并开发新的重采样方法。具体而言，本项目集中于(i)研究时间序列数据无限维参数重采样方法的高阶性质；(2)发展了统计的Edgeworth展开式理论；（iii）为规则网格上的空间数据开发新的重采样方法，旨在实现更高的阶精度；（iv）研究将重采样方法扩展到不规则空间数据并研究其高阶特性的方法。显示时空相关性的数据出现在许多科学领域，如天文学、大气科学、经济学、地质学、水文学、物理学等。使用目前的统计方法对这些数据集进行分析面临一些局限性。这主要是由于现有的统计方法主要依赖于强有力的结构（即参数模型）假设，这些假设往往不足以捕捉数据产生过程的所有重要特征。该项目旨在(i)开发新的方法（基于所谓的重采样方法），在没有强结构假设的情况下提供对不确定性的有效评估；（ii）开发理论工具，研究时间和空间相关数据统计方法的最优性。

The project focuses on investigating higher order asymptotic properties of common resampling methods for time-series and spatial data and on development of new ones. Specifically, this project concentrates on(i) investigating higher order properties of resampling methods for infinite dimensional parameters of time series data; (ii) developing Edgeworth expansion theory for statistics under long range dependence; (iii) developing new resampling methods for spatial data on a regular grid with an aim towards achieving higher order accuracy, (iv) investigating ways to extend resampling methodology to irregularly spaced spatial dataand study their higher order properties.Data exhibiting temporal and spatial dependence appear in many areas of sciences, such as Astronomy, Atmospheric Sciences, Economics, Geology, Hydrology, Physics, etc. Analyses of such data sets using current statistical methodology face some limitations. This is primarily due to the fact that the existing statistical methodology mostly rely on strong structural (i.e., parametric model) assumptions that are often inadequate to capture all important features of the data generating process. This project seeks to (i) develop new methodology (based on what are known as Resampling Methods) that provide valid assessment of uncertainty without strong structural assumptions and (ii) develop theoretical tools to investigate optimality properties of statistical methods for time- and space-dependent data.