Retrospective change point detection: From parametric to distribution free policies

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly, applied quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions.