Methods On Robust Estimation And Detection Of Multiple Outliers In Linear Regression

In medicine research, irregular points in regression will occur when actual data disagree with the distribution assumption or assumed model is wrong, and under these circumstances traditional ordinary least squares estimator will be affected or totally incorrect. In the thesis, based on some retrospective studies of modern regression analysis resources, I focus on some problems of diagnosis and influence analysis in traditional methods and try to enhance the performance of some existing methods, meanwhile some very robust regression methods are explored. So, diagnosis and remedy to the "diseased data" are provided in order to make regression analysis being correctly used in medicine research.1. The definition, history, goals of analysis and main contents of robust statistics are introduced briefly, including Huber's Minimax and llampel's infinitesimal methods. Robustness should be deemed no less important than consistency, efficiency and unbias properties in evaluation for a modern statistical method, and the traditional method is a special case in the robust.method family.2. Based on robust statistics theory some robust or resistant regression techniques are reviewed and discussed further, then the methods and robustness properties of M, GM, Wilcoxon's rank-based R and some high breakdown points estimators with two-phase procedures for linear regression model are studied in detail, including the algorithms for their estimations and hypothesis tests. In that, a new scale estimator Sn, which...