Robust Statistics for Correlated Data

North Carolina State University, Raleigh NC

Investigators

Abstract

Abstract DMS-0204297 PI: M. Genton Title: Robust Statistics For Correlated Data This 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.