Local significant differences from nonparametric two-sample tests

TL;DR: In this paper, the authors establish a framework to investigate the local differences of two multivariate data samples, as measured by a statistically significant two-sample test, and identify the locally significant difference regions by computing local test statistics based on the squared difference of two kernel density estimators.

Abstract: We establish a framework to investigate the local differences of two multivariate data samples, as measured by a statistically significant two-sample test. This framework identifies the locally significant difference regions by computing local test statistics based on the squared difference of two kernel density estimators. The key differences between the data samples are concentrated in these significantly different regions. We illustrate the visualisation and interpretation of local significant differences for simulated data, and their potential in the role of biomarker discovery for biological/biomedical data.