B0565
Title: High-dimensional change-point detection using generalized homogeneity metrics
Authors: Shubhadeep Chakraborty - University of Washington, Seattle, USA (United States) [presenting]
Xianyang Zhang - Texas A\&M University (United States)
Abstract: Change-point detection has been a classical problem in statistics and econometrics. The focus is on the problem of detecting abrupt distributional changes in the data-generating distribution of a sequence of high-dimensional observations, beyond the first two moments. This has remained a substantially less explored problem in the existing literature, especially in the high-dimensional context, compared to detecting changes in the mean or the covariance structure. We develop a nonparametric methodology to (i) detect an unknown number of change-points in an independent sequence of high-dimensional observations and (ii) test 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 other existing procedures is illustrated via extensive simulation studies as well as overstock prices data observed during the period of the Great Recession in the United States.
