Two-SampleTests based on Depth Functions

Depth functions provide measures of the deepness of a point with respect to a given set of observations. This non-parametric concept can be applied in spaces of any dimension and entails a center-outward ordering for the given data. In 1993 Liu and Singh published a new idea for a Wilcoxon-type two-sample test considering generalised depth-based ranks and in 2006 Zuo and He proved the test statistic to be asymptotically normal. Our aim is to construct change point tests by means of this Liu-Singh statistic and to investigate their asymptotic properties. Those tests that prove beneficial should be implemented such that a performant evaluation is enabled. In particular, we are interested in the behaviour of tests for high-dimensional or functional data.