Mathematical Sciences: Sampling Plans, Asymptotic Results, Resampling Algorithms, & Applications to Random Processes on the 3-dimensional Sphere

数学科学：抽样计划、渐近结果、重抽样算法、

• 批准号: 9404130
• 负责人: Jason Brown
• 金额: $ 6万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404130&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Sampling; Plans; Asymptotic

To: "Alan J. Izenman" [e-mail] From: [e-mail] (Alan J. Izenman) Subject: Brown Abstract Cc: Bcc: X-Attachments: 9404130 Brown Research on an isotropic random field on the sphere has mainly focused on the representation of the random field, although, there has been some research on proving a central limit theorem (CLT) for a continuously indexed random field on the sphere. From a practical point of view, however, it is impossible to sample continuously throughout the sphere and a finite global sampling plan needs to be found in order to investigate statistical relations associated with global data, in particular a CLT and resampling algorithms. Work by Brown 1993 lays the groundwork for future research in this area and he has applied his research to global land-area and coastline data. His work addresses the above statistical issues in a nonparametric setting using weak general conditions as the radius of the sphere grows without bound with the sample size. More recently, in the parametric setting there has been work done on modeling the entire random process on the sphere. This research will consider both nonparametric and parametric cases and asymptotic results for situations where the radius of the sphere remains fixed while the sampling plan gets more dense on the sphere and where the radius of the sphere grows without bound along with the sample size. Specifically, this research will study the following areas: finite global sampling plans, asymptotic results for different sampling plans and general statistics, resampling mechanisms of the data for various sampling plans, and applications to this new research. Typically, we only have an opportunity to sample data at a finite number of points on the globe, comprising a global sampling plan. Once a sampling plan is established, data is gathered at the points and quantities of interest are calculated. In order to make decisions about the quantity of interest, some of its characteristics need to be known or estimated. Since gathering data via the sampling process is expensive, some methods for reusing (resampling) the original data need to be developed as well. This research will study the following areas: global sampling plans, characteristics for various quantities of interest, resampling mechanisms for global data, and applications to this new research.

收件人：“Alan J. Izenman”[e-mail]发件人：[e-mail]（Alan J. Izenman）Subject：Brown Abstract Cc：Bcc：X-Bit：9404130 Brown对球面上各向同性随机场的研究主要集中在随机场的表示上，尽管已经有一些研究证明了球面上连续索引随机场的中心极限定理（CLT）。然而，从实际的角度来看，这是不可能的，在整个领域连续采样和有限的全球抽样计划需要找到，以调查与全球数据，特别是CLT和rescent算法的统计关系。布朗1993年的工作为这一领域的未来研究奠定了基础，他已将他的研究应用于全球陆地面积和海岸线数据。他的工作解决了上述统计问题，在非参数设置使用弱一般条件的半径的球体增长没有约束的样本大小。最近，在参数设置中，已经完成了对球体上的整个随机过程建模的工作。本研究将考虑非参数和参数的情况下，球的半径保持固定的情况下，而抽样计划得到更密集的球体和球体的半径增长没有约束沿着与样本量的渐近结果。具体而言，本研究将研究以下几个方面：有限的全球抽样计划，渐近结果为不同的抽样计划和一般统计，resception机制的数据为各种抽样计划，并应用到这一新的研究。 通常情况下，我们只有机会在地球仪上的有限数量的点上对数据进行采样，包括全球采样计划。一旦建立了抽样计划，就在各点收集数据，并计算感兴趣的数量。为了对感兴趣的数量做出决定，需要知道或估计它的一些特性。由于通过采样过程收集数据的成本很高，因此还需要开发一些重新使用（重新存储）原始数据的方法。本研究将研究以下领域：全球抽样计划，各种感兴趣的数量的特性，全球数据的恢复机制，以及这项新研究的应用。