A0315
Title: Statistical inference for change points in high-dimensional data
Authors: Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States)
Stanislav Volgushev - University of Toronto (Canada)
Runmin Wang - Southern Methodist University (United States) [presenting]
Changbo Zhu - University of California Davis (United States)
Abstract: Estimation and testing of change points in high-dimensional data have wide applications in many disciplines, such as biological science, economics and finance. We introduce a new U-statistic based approach to both problems and show its advantage over several existing methods via theory and simulations. The talk consists of two parts. In the first part, we will introduce a new test based on U-statistics for testing a mean shift in high-dimensional data. The test aims to detect dense alternatives and is tuning parameter-free. At the core of our theory, we show weak convergence of a sequential U-statistic based process and derive the limiting distribution under both the null and alternatives. In the second part, we will discuss a change point location estimator which maximizes a new U-statistic based objective function. Under mild and easily interpretable assumptions, we derive its convergence rate and asymptotic distribution after suitable centering and normalization. A comparison with the popular least-squares based approach illustrates our theoretical advantage. A bootstrap-based approach is also proposed to construct a confidence interval with accurate coverage, which is corroborated by simulation results. We shall illustrate our method using a real data example.
