Generalized composite multi-sample tests for high-dimensional data

High-dimensional data is ubiquitous in studies involving omics, human movement, and imaging. A multivariate comparison method is proposed for such types of data when either the dimension or the replication size substantially exceeds the other. A testing procedure is introduced that centers and scales a composite measure of distance statistic among the samples to appropriately account for high dimensions and/or large sample sizes. The properties of the test statistic are examined both theoretically and empirically. The proposed procedure demonstrates superior performance in simulation studies and an application to confirm the involvement of previously identified genes in the stages of invasive breast cancer.