Open Access
2024 Two-sample and change-point inference for non-Euclidean valued time series
Feiyu Jiang, Changbo Zhu, Xiaofeng Shao
Author Affiliations +
Electron. J. Statist. 18(1): 848-894 (2024). DOI: 10.1214/24-EJS2218


Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal dependence, we advance the self-normalization (SN) technique [22] to the inference of non-Euclidean time series, which is substantially different from the existing SN-based inference for functional time series that reside in Hilbert space [33]. Theoretically, we propose new regularity conditions that could be easier to check than those in the recent literature, and derive the limiting distributions of the proposed test statistics under both null and local alternatives. For change-point detection problem, we also derive the consistency for the change-point location estimator, and combine our proposed change-point test with wild binary segmentation to perform multiple change-point estimation. Numerical simulations demonstrate the effectiveness and robustness of our proposed tests compared with existing methods in the literature. Finally, we apply our tests to two-sample inference in mortality data and change-point detection in cryptocurrency data.

Funding Statement

F. Jiang is supported by NSFC No. 12201124, 12331009, 72271060 (China) and Shanghai Sailing Program No. 22YF1402400. X. Shao is partially supported by NSF grants DMS-2014018 and DMS-2210002.


We would like to express our sincere gratitude for the insightful and constructive comments from editors and referees.


Download Citation

Feiyu Jiang. Changbo Zhu. Xiaofeng Shao. "Two-sample and change-point inference for non-Euclidean valued time series." Electron. J. Statist. 18 (1) 848 - 894, 2024.


Received: 1 December 2022; Published: 2024
First available in Project Euclid: 26 February 2024

Digital Object Identifier: 10.1214/24-EJS2218

Keywords: change-point detection , Fréchet mean , functional data , random objects , temporal dependence

Vol.18 • No. 1 • 2024
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