December 2022 Two-sample tests for multivariate repeated measurements of histogram objects with applications to wearable device data
Jingru Zhang, Kathleen R. Merikangas, Hongzhe Li, Haochang Shou
Author Affiliations +
Ann. Appl. Stat. 16(4): 2396-2416 (December 2022). DOI: 10.1214/21-AOAS1596


Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over multiple days. It remains of great interest to appropriately evaluate how the daily distribution of biosignals might differ across disease groups and demographics. Hence, these data could be formulated as multivariate complex object data, such as probability densities, histograms, and observations on a tree. Traditional statistical methods would often fail to apply, as they are sampled from an arbitrary non-Euclidean metric space. In this paper we propose novel, nonparametric, graph-based two-sample tests for object data with the same structure of repeated measures. We treat the repeatedly measured object data as multivariate object data, which requires the same number of repeated observations per individual but eliminates any assumptions on the errors of the repeated observations. A set of test statistics are proposed to capture various possible alternatives. We derive their asymptotic null distributions under the permutation null. These tests exhibit substantial power improvements over the existing methods while controlling the type I errors under finite samples as shown through simulation studies. The proposed tests are demonstrated to provide additional insights on the location, inter- and intra-individual variability of the daily physical activity distributions in a sample of studies for mood disorders.

Funding Statement

This research was supported by the Intramural Research Program of the National Institute of Mental Health through grant ZIA MH002954-04 [Motor Activity Research Consortium for Health (mMARCH)].
Dr. Shou was supported in part by the Intergovernmental Personnel Act (IPA) from National Institute of Mental Health.
Drs. Zhang and Li wwere supported in part by NIH Grants GM129781 and GM123056.


H. Li and H. Shou contributed equally.


Download Citation

Jingru Zhang. Kathleen R. Merikangas. Hongzhe Li. Haochang Shou. "Two-sample tests for multivariate repeated measurements of histogram objects with applications to wearable device data." Ann. Appl. Stat. 16 (4) 2396 - 2416, December 2022.


Received: 1 June 2021; Revised: 1 November 2021; Published: December 2022
First available in Project Euclid: 26 September 2022

MathSciNet: MR4489216
zbMATH: 1498.62274
Digital Object Identifier: 10.1214/21-AOAS1596

Keywords: Graph-based test , non-Euclidean data , Nonparametric test , repeated measures , wearable device data

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 4 • December 2022
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