LINEAR REGRESSION ANALYSIS

Determining if a dataset has one or more outliers is a fundamental and challenging problem in statistical analysis. This dissertation introduces a statistical framework that addresses two well-known problems in the outlier analysis. The first problem (Problem 1) is to detect outliers in independent and identically distributed univariate samples, which is the basic setting of outlier problem. The second problem (Problem 2) is to detect outliers and influential observations in the linear regression analysis, which is a major topic in linear regression model diagnostics and represents a more complete setting. The proposed framework is motivated by a graphic outlier detection method proposed recently for Problem 1. It is observed in bootstrapping that some bootstrap samples contain outliers while others do not, when outliers are present in a sample. Based on this observation, the method discovers that a bootstrap sample statistic (termed “mean – trimmed mean”) is sensitive to outliers, and particularly its histogram is multimodal in the presence of outliers. Consequently outliers are detected by plotting and visually checking the histogram. Considerin