Robust Statistics for Correlated Data

摘要DMS-0204297PI：M.GentonTitle：相关数据的稳健统计这项研究集中在两个主要的新想法上。首先，通过隐式而不是显式地定义不良度量的临界区，将故障点的概念推广到相关观测，从而涵盖了不相关观测和相关观测的情况。其次，介绍了一种新的似然估计方法，该方法可以应用于任何存在参数似然的情况。这种新方法与测量误差模型密切相关，并在位置尺度独立、同分布的环境中降低到众所周知的受污染的正态似然。这一新方法将被用来推广空间数据设置中的许多常用方法。这项研究的应用包括来自环境科学的真实数据源，即美国的臭氧浓度和细颗粒物。这项工作将对时空统计学的理论统计学家和实践者产生影响，从而促进学术界和产业界之间的合作。它的目的是提供更可靠的时空数据集分析，从而有助于更好地理解控制大气传输污染物的物理过程。特别是，它将为1990年《清洁空气法》修正案中规定的立法减排的有效性提供更可靠的评估。此外，该项目将支持北卡罗来纳州立大学教授和推广稳健统计学和时空统计学。

AbstractDMS-0204297PI: M. GentonTitle: Robust Statistics For Correlated DataThis research focuses on two main new ideas. First, the concept of breakdown point is generalized to correlated observations by defining the critical region of the badness measure implicitly rather than explicitly, thus covering situations with both uncorrelated and correlated observations. Secondly, a new method to robustify likelihoods is introduced that can be applied in any situation where a parametric likelihood is available. This new approach is intimately connected to measurement error models and reduces to well-known contaminated normal likelihoods in location-scale independent, identically distributed settings. This new approach will be used to robustify many of the commonly used methods in spatial data settings.The applications of this research include real data sources from environmental sciences, namely ozone concentrations and fine particulate matter in the U.S. This work will have impact on both, theoretical statisticians and practitioners of spatio-temporal statistics, and hence will foster collaboration between academia and industry. It aims to provide more reliable analyses of spatio-temporal data sets, and thus contribute to a better understanding of physical processes governing atmospherically-transported pollutants. In particular, it will provide more reliable evaluations of the effectiveness of the legislated emission reductions mandated in the Clean Air Act Amendments of 1990. Moreover, this project will support the teaching and promotion of robust statistics and spatio-temporal statistics at North Carolina State University.