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Repeated observations have become increasingly common in biomedical researchand longitudinal studies. For instance, wearable sensor devices are deployed tocontinuously track physiological and biological signals from each individualover multiple days. It remains of great interest to appropriately evaluate howthe daily distribution of biosignals might differ across disease groups anddemographics. Hence these data could be formulated as multivariate complexobject data such as probability densities, histograms, and observations on atree. Traditional statistical methods would often fail to apply as they aresampled from an arbitrary non-Euclidean metric space. In this paper, we proposenovel non-parametric graph-based two-sample tests for object data with repeatedmeasures. A set of test statistics are proposed to capture various possiblealternatives. We derive their asymptotic null distributions under thepermutation null. These tests exhibit substantial power improvements over theexisting methods while controlling the type I errors under finite samples asshown through simulation studies. The proposed tests are demonstrated toprovide additional insights on the location, inter- and intra-individualvariability of the daily physical activity distributions in a sample of studiesfor mood disorders.

Two-sample tests for repeated measurements of histogram objects with applications to wearable device data