Selected aspects of robust regression and comparison of robust regression methods

This dissertation examines the robust regression methods. The primary purpose of this work is to propose an extension, derivation and summary (including computational algorithm) for Theil-Sen's regression estimates (or in some literature also referred to as Passing-Bablok's regression method) for multi-dimensional space and compare this method to other robust regression methods. The combination of these two objectives is the primary and the original contribution of the dissertation. Based on the available literature it is unknown if anyone has discussed this problem in greater depth and solved it in total. Therefore this work provides a summary overview of the issue and offers a new alternative of this multidimensional, nonparametric, robust regression method. Secondary goals include a clear summary of other robust methods, a summary of findings related to these robust regression methods, robust methods compared with each other placing emphasis on the comparison with the proposed Theil-Sen's regression estimates method and with the least squares method. The summary also includes individual mathematical context and interchangeability of the proposed methods. These secondary objectives are also another benefit of this dissertation in the field of robust regression problems; this is especially important to gain a unified view of the problems of robust regression methods and estimates in general.