B0966
Title: Depth-based two-sample testing
Authors: Felix Gnettner - Otto-von-Guericke-Universitaet Magdeburg (Germany) [presenting]
Claudia Kirch - Otto-von-Guericke University Magdeburg (Germany)
Alicia Nieto-Reyes - Universidad de Cantabria (Spain)
Abstract: 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. A two-sample test has been previously proposed that is based on depth-ranks and offers opportunities for further investigations: Observing that the corresponding test statistic $Q(X, Y)$ is not symmetric with respect to the two samples $X$ and $Y$, the power can be greatly increased if $Q(X, Y)$ and $Q(Y, X)$ are jointly considered. Within the last years, depths with respect to functional data have been established that we combine with this procedure to obtain new non-parametric two-sample tests for functional data. We investigate the asymptotic behaviour of this modified test procedure for several classes of depths including depths for functional data.
