Plenary Lecture

Detection of Changes in Dependent Processes: Learning from Algorithms, Simulations and Stochastic Inference

Professor Ansgar Steland
RWTH Aachen University

Abstract: Many present day data are sequentially observed discrete-time processes, i.e. they represent data streams where the data associated to the $n$th time instant is available with negligible delay. The problem to design and study monitoring procedures which aim at detecting changes in the structure of the process has recently received substantial and growing interest. We provide an overview of recent advances in the construction of methods for change detection and their asymptotic distribution theory, which allows us to construct detection procedures with well-defined nominal statistical properties. A powerful and elegant mathematical approach is to establish limit theorems by showing that the detection algorithm of interest, often motivated by a statistical method of estimation applied to a specific distributional model, is induced (or can be approximated) by a smooth functional of a basic stochastic process such as the partial sum process or the characteristic process. In this way, one can obtain asymptotic results that hold true for rich nonparametric classes of time series. Further, we discuss simulation approaches that provide accurate distributional estimates for practical applications in cases where the asymptotic limit process is intractable. In this way, combining stochastic limit theory, simulation and applications provide a powerful approach to learn from data.

Brief Biography of the Speaker: Ansgar Steland received the M.Sc. and Ph.D. degrees in mathematics from the University of Gottingen Germany, in 1993 and 1996, respectively. He held positions as an assistant at the Technical University of Berlin, Berlin, Germany, as a consultant in industry, as a postdoc at the European University Viadrina of Frankfurt/Oder, Germany, and as a lecturer at the Faculty of Mathematics at the Ruhr-University Bochum, where he also led the statistical consulting services. Since 2006, he has been a Professor at RWTH Aachen University, Germany, where he holds the Chair of Stochastics at the Institute of Statistics. Dr. Steland has been member of several societies, headed the Department of Mathematics from 2010 to 2012, acts as the chair of the Society for Reliability, Quality and Safety, and also chairs the Working Group of Change-Point Analysis of the German Statistical Society. His current research interests are in nonparametric regression, signal and change-point detection, sequential analysis and quality control, applications to photovoltaics, empirical stochastic processes, econometrics, and time series analysis.