Multiscale Quantile Segmentation

Jula Vanegas L, Behr M, Munk A (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Journal of the American Statistical Association American Statistical Association / Taylor & Francis

Book Volume: 117

Pages Range: 1384-1397

Journal Issue: 539

DOI: 10.1080/01621459.2020.1859380

Abstract

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. Supplementary materials for this article are available online.

Involved external institutions

Georg-August-Universität Göttingen DE Germany (DE) University of California, Berkeley US United States (USA) (US)

How to cite

APA:

Jula Vanegas, L., Behr, M., & Munk, A. (2022). Multiscale Quantile Segmentation. Journal of the American Statistical Association, 117(539), 1384-1397. https://dx.doi.org/10.1080/01621459.2020.1859380

MLA:

Jula Vanegas, Laura, Merle Behr, and Axel Munk. "Multiscale Quantile Segmentation." Journal of the American Statistical Association 117.539 (2022): 1384-1397.

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