One-sample location tests based on center-outward signs and ranks

Abstract: A multivariate one-sample location test based on the center-outward ranks and signs is considered, and two different testing procedures are proposed for centrally symmetric distributions. The first test is based on a random division of the data into two samples, while the second one uses a symmetrized sample. The asymptotic distributions of the proposed tests are provided. For univariate data, two variants of the symmetrized test statistic are shown to be equivalent to the standard sign and Wilcoxon test respectively. The small sample behavior of the proposed techniques is illustrated by a simulation study that also provides a power comparison for various transportation grids.