Efficient ANOVA for directional data

In this paper, we tackle the ANOVA problem for directional data. We apply the invariance principle to construct locally and asymptotically most stringent rank-based tests. Our semi-parametric tests improve on the optimal parametric tests by being valid under the whole class of rotationally symmetric distributions. Moreover, they keep the optimality property of the latter under a given m-tuple of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation. We conclude by applying our findings to a real-data example involving geological data.