Robust model selection and outlier detection in linear regressions

Abstract

In this thesis, we study the problems of robust model selection and outlier detection in linear regression. The results of data analysis based on linear regressions are highly sensitive to model choice and the existence of outliers in the data. This thesis aims to help researchers to choose the correct model when their data could be contaminated with outliers, to detect possible outliers in their data, and to study the impact that such outliers have on their analysis. First, we discuss the problem of robust model selection. Many methods for performing model selection were designed with the standard error model ... and least squares estimation in mind. These methods often perform poorly on real world data, which can include outliers. Robust model selection methods aim to protect us from outliers and capture the model that represents the bulk of the data. We review the currently available model selection algorithms (both non-robust and robust) and present five new algorithms. Our algorithms aim to improve upon the currently available algorithms, both in terms of accuracy and computational feasibility. We demonstrate the improved accuracy of our algorithms via a simulation study and a study on a real world data set.

(cont.) Finally, we discuss the problem of outlier detection. In addition to model selection, outliers can adversely influence many other outcomes of regression-based data analysis. We describe a new outlier diagnostic tool, which we call diagnostic data traces. This tool can be used to detect outliers and study their influence on a variety of regression statistics. We demonstrate our tool on several data sets, which are considered benchmarks in the field of outlier detection.