Title: Variations of the depth based Liu-Singh two-sample test including functional spaces
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: Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a non-parametric concept applicable to spaces of any dimension, for instance, multivariate and functional. A multivariate two-sample test exists based on depth-ranks. The objective is to improve the power of the associated test statistic and incorporate its applicability to functional data. In doing so, we obtain a more natural test statistic that is symmetric in both samples. We derive the null asymptotic of the proposed test statistic, also proving the validity of the testing procedure for functional data. Finally, the finite sample performance of the test with several different depth functions for multivariate as well as functional data is illustrated by means of a simulation study.