  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 non-parametric graph-based two-sample tests for 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 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.
