Multiscale Quantile Segmentation

• 成果类型: Article
• 署名作者: Jula Vanegas, Laura; Behr, Merle; Munk, Axel
• 署名单位: University of Gottingen; University of California System; University of California Berkeley; Max Planck Society
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1859380
• 发表日期: 2022
• 页码: 1384-1397
• 关键词: change-point detection; nonparametric approach; number; MULTIVARIATE; regression; computation; inference; cancer

摘要

We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial independence. It is based on a multiscale statistic, which allows to control the (finite sample) probability for selecting the correct number of segments S at a given error level, which serves as a tuning parameter. For a proper choice of this parameter, this probability tends exponentially fast to one, as sample size increases. We further show that the location and size of segments are estimated at minimax optimal rate (compared to a Gaussian setting) up to a log-factor. Thereby, our approach leads to (asymptotically) uniform confidence bands for the entire quantile regression function in a fully nonparametric setup. The procedure is efficiently implemented using dynamic programming techniques with double heap structures, and software is provided. Simulations and data examples from genetic sequencing and ion channel recordings confirm the robustness of the proposed procedure, which at the same time reliably detects changes in quantiles from arbitrary distributions with precise statistical guarantees. for this article are available online.