Adaptive Inference for Change Points in High-Dimensional Data

• Activity Number: 201 - Nonparametric Statistics Student Paper Competition Presentations
• Type: Topic-Contributed
• Date/Time: Tuesday, August 10, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yangfan Zhang* and Runmin Wang and Xiaofeng Shao
• Companies: University of Illinois at Urbana-Champaign and Southern Methodist University and University of Illinois at Urbana-Champaign
• Keywords: asymptotically pivotal; segmentation; self-normalization; structural break; U-statistics

Abstract

In this talk, I will present a new class of test statistics for a change point in the mean of high-dimensional independent data proposed in our paper. Our test integrates the U-statistic based approach and Lq-norm based high-dimensional test, and inherits several appealing features such as being tuning parameter free and asymptotic independence for test statistics corresponding to even q's. A simple combination of test statistics corresponding to several different q's leads to a test with adaptive power property, that is, it can be powerful against both sparse and dense alternatives. On the estimation front, we obtain the convergence rate of the maximizer of our test statistic standardized by sample size when there is one change-point in mean and q=2, and propose to combine our tests with a wild binary segmentation (WBS) algorithm to estimate the change-point number and locations when there are multiple change-points. Numerical comparisons using both simulated and real data demonstrate the advantage of our adaptive test and its corresponding estimation method.