Inference in High-Dimensional Online Changepoint Detection

• 成果类型: Article
• 署名作者: Chen, Yudong; Wang, Tengyao; Samworth, Richard J.
• 署名单位: University of Cambridge; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2199962
• 发表日期: 2024
• 页码: 1461-1472
• 关键词: change-point detection; confidence-intervals; SPARSE; tests

摘要

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the U.S. excess deaths data from 2017 to 2020. The , which contains the proofs of our theoretical results, is available online.