  Statistical depth functions provide measures of the outlyingness, or
centrality, of the elements of a space with respect to a distribution. It is a
nonparametric concept applicable to spaces of any dimension, for instance,
multivariate and functional. Liu and Singh (1993) presented a multivariate
two-sample test based on depth-ranks. We dedicate this paper to improving the
power of the associated test statistic and incorporating 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 for functional data is
illustrated by means of a simulation study and a real data analysis on annual
temperature curves of ocean drifters is executed.
