On some validity-robust tests for the homogeneity of concentrations on spheres

Abstract

In this paper we tackle the problem of testing the homogeneity of concentrations for directional data. All the existing procedures for this problem are parametric procedures based on the assumption of a Fisher–von Mises–Langevin (FvML) distribution. We construct here a pseudo-FvML test and a rank-based Kruskal–Wallis-type test for this problem. The pseudo-FvML test improves on the traditional FvML parametric procedures by being asymptotically valid under the whole semiparametric class of rotationally symmetric distributions. Furthermore, it is asymptotically equivalent to the locally and asymptotically most stringent parametric FvML procedure in the FvML case. The Kruskal–Wallis rank-based test is also asymptotically valid under rotationally symmetric distributions and performs nicely under various important distributions. The finite-sample behaviour of the proposed tests is investigated by means of a Monte Carlo simulation.

Keywords:

• directional statistics
• homogeneity of concentrations
• rank-based tests
• robusttests

Disclosure

No potential conflict of interest was reported by the authors.