Title: High-dimensional change-point detection using generalized distance metrics
Authors: Shubhadeep Chakraborty - Texas A and M University (United States)
Xianyang Zhang - Texas A\&M University (United States) [presenting]
Abstract: Change-point detection has been a classical problem in statistics, finding applications in a wide variety of fields. A nonparametric change-point detection procedure is concerned with detecting abrupt distributional changes in the data generating distribution, rather than only changes in mean. We consider the problem of detecting an unknown number of change-points in an independent sequence of high-dimensional observations and testing for the significance of the estimated change-point locations. Our approach essentially rests upon nonparametric tests for the homogeneity of two high-dimensional distributions. We construct a single change-point location estimator via defining a cumulative sum process in an embedded Hilbert space. As the key theoretical innovation, we rigorously derive its limiting distribution under the high dimension medium sample size (HDMSS) framework. Subsequently, we combine our statistic with the idea of wild binary segmentation to recursively estimate and test for multiple change-point locations. The superior performance of our methodology compared to several other existing procedures is illustrated via both simulated and real datasets.