Inference based on data depth by Rainer Dyckerhoff

Abstract

Tests which are based on the rank statistic play an important role in univariate nonparametric statistics. The rank statistic of a sample assigns to each sample variable its position in the order statistic. If one tries to generalize rank tests to the multivariate case, one is faced with the problem of defining a multivariate order statistic. Because of the absence of a natural linear order on ℝ^d it is not clear how to define a multivariate order or rank statistic in a meaningful way.