Spatial and Spatio-temporal Processes: Asymptotics, Misspecification and Multivariate Extension

空间和时空过程：渐近、错误指定和多元扩展

• 批准号: 0833323
• 负责人: Hao Zhang
• 金额: $ 15.21万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-02-27 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0833323&HistoricalAwards=false
• 关键词: Spatial; Spatio; temporal; Processes; Asymptotics

The investigator develops appropriate infill or fixed domain asymptotic results for the evaluation of approximation methods for spatial data. The infill asymptotic framework is generally preferred for spatial data. However, infill asymptotic results for estimation are in general difficult to derive, and there exist only a few explicit infill asymptotic results pertaining to specific models. In this proposal, a general approach to establishing the infill asymptotic properties is outlined and followed to establish asymptotic distributions of estimators that maximize some approximated likelihood functions such as Vecchia's approximation and covariance tapering. These infill asymptotic results assure that the approximation methods may yield asymptotically efficient estimators. In addition, for spatio-temporal data, the investigator considers a new asymptotic framework in which the temporal domain is increasing while the spatial sampling domain is fixed. Under this asymptotic framework, the investigator shows that an incorrect covariance function (such as covariance tapering) generally results in biased estimators. The investigator establishes asymptotic results that allow for the correction of biases. The adjusted estimators are expected to be asymptotically normal and unbiased. These asymptotic results allow one to employ incorrect but simpler spatio-temporal covariance functions and then adjust for the bias. Finally, the investigator extends the results from the univariate case to the multivariate case when multiple spatial variables are observed across space and/or over time.Data across space and time are routinely observed in many scientific studies that are very important to the society such as those on global warming, environmental monitoring, precision agriculture, epidemiology, hot spot detection in homeland security, etc. The immense amount of data and the correlation across space and time have raised new challenges to the modeling and analysis of such space-time data. The primary goal of this project is tackle these challenges by studying computationally feasible and efficient approaches to the analysis of vast space-time data, which also bear no or little loss of statistical efficiency. It is expected that this project will make more accessible and feasible the analysis of huge spatial and spatial-temporal data to scientists in broader disciplines, and thus enables scientists to retrieve significant and reliable information from the vast amount of data.

研究人员开发了适当的填充或固定域渐近结果，以评估空间数据的近似方法。 对于空间数据，通常首选无置渐近框架。但是，通常难以得出估计的渐近结果，并且仅存在与特定模型有关的少数显式填充渐近结果。在此提案中，概述并遵循了建立无序渐近性特性的一般方法，以建立渐近分布的估计值，以最大程度地提高一些近似可能性函数，例如Vecchia的近似和协方差渐变。这些无置渐近结果确保近似方法可能产生渐近有效的估计器。此外，对于时空数据，研究人员认为，在固定空间采样结构域的同时，时间域增加了一个新的渐近框架。在这个渐近框架下，研究者表明，不正确的协方差函数（例如协方差逐渐减少）通常会导致估计量有偏见。研究者建立了渐近结果，可以纠正偏见。预计调整后的估计量在渐近且无偏见。这些渐近结果使人们可以采用不正确但更简单的时空协方差函数，然后调整偏差。最后，研究者将结果从单变量案例扩展到多变量案例，当时在整个空间和/或随着时间的时间上观察到多个空间变量。在许多科学研究中，常规观察到跨空间和时间的数据对社会非常重要，这些社会对诸如全球变暖，环境监测，精确的农业，流行病学，流行病学和跨越的型号的环境监测等方面的社会非常重要。已经对此类时空数据的建模和分析提出了新的挑战。该项目的主要目的是通过研究计算可行和有效的方法来分析大量时空数据，从而解决这些挑战，这些方法也没有统计效率的损失或几乎没有损失。 可以预期，该项目将使对更广泛学科的科学家对巨大的时空和时空数据的分析更容易及可行，从而使科学家能够从大量数据中检索重要和可靠的信息。