A nonparametric approach to high-dimensional k-sample comparison problems

SummaryHigh-dimensional $k$-sample comparison is a common task in applications. We construct a class of easy-to-implement distribution-free tests based on new nonparametric tools and unexplored connections with spectral graph theory. The test is shown to have various desirable properties and a characteristic exploratory flavour that has practical consequences for statistical modelling. Numerical examples show that the proposed method works surprisingly well across a broad range of realistic situations.