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

该项目侧重于检索空间数据中可能因测量误差而被掩盖的信号的方法。具体而言，研究者建议建立无偏参数估计和空间相关的数据与预测和响应中存在的错误的最佳预测，然后将解决方案应用于古气候重建，以实现过去气候的忠实代表。从拟议的工作的结果将同时考虑空间相关性和误差的变量，揭示反应和解释变量之间的真实关系。研究了在各种测量误差结构下，参数估计的偏差和渐近性态以及不同意义下的预测的最优性。此外，本文还提出了一种新的无重复数据测量误差方差-协方差矩阵的实用估计方法，为空间数据分析中变量误差的校正提供了实用的统计工具。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问题，即过去气候的振幅在理解气候系统的动力学方面起着核心作用。除了气候学之外，所提出的方法通常可以应用于各种其他学科，例如地震学、气象学、大气科学和公共卫生研究，这些学科的数据通常在空间上是相关的，并且包含大量的噪声。然而，拟议活动的广泛影响是多方面的。这项建议的一个关键方面是研究和教学的一体化，这将通过在测量误差和空间统计课程教学期间为学生提出具体项目来实现。

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.