Higher order accuracy of bootstrap methods for temporal and spatial processes

该项目的重点是调查时间序列和空间数据的常见resstriking方法的高阶特性，以及开发新的推理方法，以提高现有方法的准确性和稳定性。 具体而言，本项目集中于（i）发展Edgeworth展开理论，用于依赖下的学生化统计，（ii）研究时间序列数据的Bootstrap近似的高阶精度，（iii）发展以实现高阶精度为目标的恢复方法，（iv）经验性地选择最佳块长度的非参数方法，（v）一种产生总体参数的更稳定估计的bootstrap的汇集方法，（vi）研究空间预测问题中bootstrap近似的准确性，以及（vii）调查不规则间隔数据的空间数据的自助逼近的准确性-显示时间和空间依赖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。 这主要是因为现有的统计方法主要依赖于强结构性（即，参数模型）假设，这些假设通常不足以捕获数据的所有重要特征。 该项目旨在（i）开发新的方法（基于所谓的恢复方法），提供有效的不确定性评估，而无需强有力的结构假设，（ii）开发理论工具，以研究时间和空间相关数据的各种恢复方法的最优性。

The emphasis of the project is on investigating higher order properties of common resampling methods for time-series and spatial data and on development of new inference methods that improve the accuracy and stability of existing methods. Specifically, this project concentrates on (i) developing Edgeworth expansion theory for Studentized statistics under dependence, (ii) investigating higher order accuracy of bootstrap approximations for time series data, (iii) developing resampling methods with an aim towards achieving higher order accuracy, (iv) a nonparametric method for the selection of optimal block length empirically,(v) a pooling method for the bootstrap that yields more stable estimators of population parameters, (vi) investigating accuracy of bootstrap approximation in spatial prediction problems, and(vii) investigating accuracy of bootstrap approximation for spatial data for irregularly spaced data-points.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 relies on strong structural (i.e., parametric model) assumptions that are often inadequate to capture all important features of the data. This project seeks to(i) develop new methodology (based on what are known as Resampling Methods) that provides valid assessment of uncertainty without strong structural assumptions and (ii) develop theoretical tools to investigate optimality properties of various resampling methods for time- and space-dependent data.