Spatially Correlated Data with Errors-in-variables: Inteference and Prediction with Application to Paleoclimate Reconstruction

该项目的重点是检索空间数据中可能因测量误差而被屏蔽的信号的方法。具体地说，研究人员建议对具有预测和响应误差的空间相关数据建立无偏参数估计和最优预测，然后将这些解决方案应用于古气候重建，以实现对过去气候的真实表示。这项工作的结果将同时考虑空间相关性和变量中的误差，以揭示响应和解释变量之间的真实关系。在不同的测量误差结构下，研究了参数估计的偏差和渐近行为以及不同意义下预测的最优性。此外，还提出了一种新的实用的无重复数据测量误差方差-协方差矩阵的估计方法，该项目的主要影响是为空间数据分析中变量误差的影响提供实用的统计工具。一旦这些结果被应用于古气候重建，它们将解决一个长期存在的关于过去气候幅度的问题，这个问题在理解气候系统的动态方面发挥着核心作用。除了气候学，建议的方法还可以普遍应用于各种其他学科，如地震学、环境计量学、大气科学和公共卫生研究，这些领域的数据通常在空间上相关，并包含大量噪音。然而，拟议活动的更广泛影响是多方面的。这一建议的一个关键方面是研究与教学的结合，将通过在有关测量误差和空间统计的课堂教学中为学生提出具体的项目来实现这一点。

The project focuses on methods to retrieve signals in spatial data that are possibly masked due to measurement errors. Specifically, the investigator proposes to establish unbiased parameter estimates and optimal predictions for spatially correlated data with errors present in both predictors and responses, and then apply the solutions to paleoclimate reconstruction to achieve a faithful representation of the past climate. The results from the proposed work will take both the spatial correlation and errors-in-variables into account to uncover the true relationship between the response and explanatory variables. The bias and the asymptotic behavior of the parameter estimates and the optimality of predictions in different senses under various measurement error structures are investigated. Besides, a new practical method for estimating the variance-covariance matrix of measurement errors for data with no replicates is proposed.The primary impact of this project is to provide practical statistical tools to correct the effects of errors-in-variables in spatial data analysis. Once the results are applied to paleoclimate reconstructions, they will solve a long standing problem concerning the amplitudes of past climate that plays a central role in understanding the dynamics of the climate system. In addition to climatology, the proposed methods can be generally applied to a variety of other disciplines such as seismology, environmetrics, atmospheric sciences and public health studies, where data are usually spatially correlated and contain substantial noise. However, the broader impacts of the proposed activities are multiple. A key aspect of this proposal is the integration of research and teaching, which will be achieved by proposing specific projects for students during the teaching of classes on measurement errors and on spatial statistics.