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

时空过程的重采样方法及其高阶精度

• 批准号: 0707139
• 负责人: Soumendra Lahiri
• 金额: $ 31.93万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0707139&HistoricalAwards=false
• 关键词: Resampling; methods; temporal; spatial; processes

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.

该项目的重点是调查时间序列和空间数据的常用重建方法的高阶渐近性质，并开发新的方法。本计画的主要目的为：（i）研究时间序列资料之无穷维参数的重数方法的高阶性质;（ii）发展长程相依统计量的Edgeworth展开理论;（iii）为规则格网上的空间数据开发新的重定位方法，以达到更高的精度，（iv）研究如何将恢复方法扩展到不规则间隔的空间数据并研究其高阶性质。表现出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、使用目前的统计方法对这些数据集进行分析面临着一些局限性。这主要是因为现有的统计方法大多依赖于强结构性（即， 参数模型）假设，这些假设通常不足以捕获数据生成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Rescue方法），在没有强有力的结构假设的情况下提供有效的不确定性评估，以及（ii）开发理论工具来研究最优性 时间和空间相关数据的统计方法的特性。