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

该项目的重点是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以及新方法的发展。具体地说，本项目致力于：(1)研究时间序列数据无限维参数重采样方法的高阶性质；(2)发展长相关下统计学的Edgeworth展开理论；(3)发展新的规则网格空间数据重采样方法，以达到更高的阶次精度；(4)研究如何将重采样方法扩展到不规则间隔的空间数据并研究其高阶特性。数据表现出时间和空间相关性的许多科学领域，如天文学、大气科学、经济学、地质学、水文学、物理学等。使用现有统计方法分析这类数据集面临一些局限性。这主要是因为现有的统计方法大多依赖于强有力的结构性(即参数模型)假设，而这些假设往往不足以反映数据生成过程的所有重要特征。该项目力求(1)开发新的方法(以所谓的重抽样方法为基础)，在没有强有力的结构性假设的情况下提供对不确定性的有效评估；(2)开发理论工具，以研究依赖时间和空间的数据的统计方法的最优化性质。

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.