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

TL;DR

This paper introduces new multivariate one-sample location tests using center-outward ranks and signs, providing asymptotic distributions and demonstrating their effectiveness through simulations.

Contribution

It proposes two novel testing procedures for multivariate data based on center-outward ranks and signs, with asymptotic analysis and simulation validation.

Findings

Asymptotic distributions of the tests are derived.

The tests perform well in small samples according to simulations.

For univariate data, the tests are equivalent to classical sign and Wilcoxon tests.

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.