TWO-SAMPLE TESTS FOR MULTIVARIATE REPEATED MEASUREMENTS OF HISTOGRAM OBJECTS WITH APPLICATIONS TO WEARABLE DEVICE DATA

• 成果类型: Article
• 署名作者: Zhang, Jingru; Merikangas, Kathleen R.; Li, Hongzhe; Shou, Haochang
• 署名单位: University of Pennsylvania; National Institutes of Health (NIH) - USA; NIH National Institute of Mental Health (NIMH)
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/21-AOAS1596
• 发表日期: 2022
• 页码: 2396-2416
• 关键词: physical-activity; AGE; DEPRESSION; covariance; patterns

摘要

Repeated observations have become increasingly common in biomedi-cal 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 appropri-ately 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 re-peatedly measured object data as multivariate object data, which requires the same number of repeated observations per individual but eliminates any as-sumptions 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 pro-posed tests are demonstrated to provide additional insights on the location, inter-and intra-individual variability of the daily physical activity distribu-tions in a sample of studies for mood disorders.