New Non-parametric Tests for Multivariate Paired Data
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Paired data are common in many fields, such as medical diagnosis and longitudinal data analysis, where measurements are taken for the same set of objects under different conditions. In many of these studies, the number of measurements could be large. Existing methods either impose strong assumptions or have power decrease fast as the number of measurements increases. In this work, we propose new non-parametric tests for paired data. These tests exhibit substantial power improvements over existing methods under moderate- to high- dimensional data. 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 data set on the Alzheimer's disease research.
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