Two-Sample Tests for Object Data with Repeated Measures

• Activity Number: 336 - Nonparametric Test in Unusual Data Structure or of Independence
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jingru Zhang* and Hongzhe Li and Haochang Shou
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: Graph-based test; Nonparametric test; Non-Euclidean data; Wearable device data

Abstract

Data with repeated measures are common in many fields, such as medical diagnosis and longitudinal data analysis, where measurements are taken several times on the same set of subjects. In many of these studies, data come from an arbitrary metric space, which may not be Euclidean, for example, probability distributions in the Wasserstein space. Existing methods either simplify the repeated measures to only one measure for each subject or cannot be applied to non-Euclidean datasets. In this work, we propose new non-parametric tests for data with repeated measures. These tests exhibit substantial power improvements over existing methods on different types of data and under various alternatives. We also derived asymptotic distributions of the new tests and the approximate p-values based on them are reasonably accurate under finite samples through simulation studies, making the new tests easy-off-the-shelf tools for real applications. The proposed tests are illustrated through the analysis of a real dataset on bipolar disorder research.