Robust Statistics for Correlated Data

摘要DMS-0204297 PI：M. GentonTitle：Robust Statistics For Correlated Data相关数据的稳健统计本研究主要关注两个新的观点。首先，击穿点的概念被推广到相关的观察定义的不良措施的临界区域隐含而不是明确的，从而涵盖的情况下，不相关和相关的观察。其次，介绍了一种新的鲁棒似然方法，该方法可以应用于任何参数似然可用的情况。这种新的方法是密切相关的测量误差模型，并减少到众所周知的污染正常的可能性，在位置尺度独立，同分布的设置。这种新的方法将被用来robustify许多常用的方法在空间数据settings.The应用程序的研究，包括真实的数据来源，从环境科学，即臭氧浓度和细颗粒物在美国这项工作将产生影响，理论统计学家和从业人员的时空统计，因此将促进学术界和工业界之间的合作。其目的是提供更可靠的时空数据集分析，从而有助于更好地了解大气传输污染物的物理过程。特别是，它将对1990年《清洁空气法修正案》规定的立法减排的有效性提供更可靠的评估。此外，该项目还将支持北卡罗来纳州州立大学教授和推广稳健统计和时空统计。

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.