A general analysis of change-point methods

Abstract

The primary goal of this report is to provide a general overview of offline change-point literature as it is known today. Change-point methods are important statistical problems, where we are interested in determining whenever a certain data-set changes in structure. Furthermore, the term "off-line" is meant to indicate that the data itself is already known, whereas on the other hand we have "on-line" methods which deal with situations where new data is yet being received during localisation of the change-points. In this report we mainly consider off-line methods, as we feel off-line methods provide a more friendly introduction into change-point analysis and on-line methods are in principle just an extension of their off-line counterparts. First off, these off-line change-point methods are considered under different assumptions (parametric, non-parametric). In each case, we treat a solution to the change-point problem under different models(normal and gamma model, mean or varianche change etc.). Eventually we shall also treat some widely used algorithms, meant to extend the problem into the localisation of multiple change-points.indent Aside from theoretical considerations, an equally important part of this report will be focused on empirical results. Both for the statistics as algorithms will there be a performance study where the different methods will be empirically assessed and compared under different models, namely the robustness against "outliers"(extreme data-values) will be investigated. So to complement the primary goal, we will also focus on the following two subgoals:
1) Assessment and comparison of different change-point models
2) Evaluating and improving robustness against outliers