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Math & Stats Department Colloquium

Friday, April 8th, 2022

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Runmin Wang (Southern Methodist University)

Title: Statistical Inference for Change Points in High-Dimensional Data

Abstract: Estimation and testing of change points in high-dimensional data have wide applications in many disciplines, such as biological science, economics and finance. In this talk, 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 the theoretical advantage of ours. 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 at the end of the talk.

Runmin Wang is an Assistant Professor in the Department of Statistical Science at Southern Methodist University. He got his Ph.D. in Statistics from the University of Illinois at Urbana-Champaign in 2020. His research interests include change point inference, high-dimensional data and time series analysis.