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Title: Two-sample tests for repeated measurements of histogram objects in wearable device data Authors:  Jingru Zhang - University of Pennsylvania (United States)
Hongzhe Li - University of Pennsylvania (United States)
Haochang Shou - University of Pennsylvania (United States) [presenting]
Abstract: Repeated measures of wearable sensor data over multiple days have become increasingly available in biomedical research and longitudinal studies. Additionally, those data often have complex multivariate structures that are from an arbitrary non-Euclidean metric space. In particular, we will be investigating the probability densities of daily physical activity measures as densely assessed by accelerometers. Those object data are sampled from a bounded metric space and cannot be analyzed using traditional statistical methods. We propose novel non-parametric graph-based two-sample tests for the activity density object data with repeated measures. 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 existing methods under various alternative hypotheses and are shown to preserve the type I errors under finite samples, as shown through simulation studies. We apply the proposed tests to differentiate the distributions of daily physical activity profiles from a study population of mood disorders.