On robust estimation of multiple change points in multivariate and matrix processes
There are numerous areas of human activities where various processes are observed over time. If the conditions of the process change, it can be reflected through the shift in observed response values. The detection and estimation of such shifts is commonly known as change point inference. While the estimation helps us learn about the process nature, assess its parameters, and analyze identified change points, the detection focuses on finding shifts in the real-time process flow. There is a vast variety of methods proposed in the literature to target change point detections in both settings. Unfortunately, the majority of procedures impose very restrictive assumptions. Some of them include the normality of data, independence of observations, or independence of subjects in multisubject studies. In this dissertation, a new methodology, relying on more realistic assumptions, is developed. This dissertation report includes three chapters. The summary of each chapter is provided below. In the first chapter, we develop methodology capable of estimating and detecting multiple change points in a multisubject single variable process observed over time. In the second chapter, we introduce methodology for the robust estimation of change points in multivariate processes observed over time. In the third chapter, we generalize the ideas presented in the first two chapters by developing methodology capable of identifying multiple change points in multisubject matrix processes observed over time.