Efficient ANOVA for Directional Data

In this paper we tackle the ANOVA problem for directional data (with particular emphasison geological data) by having recourse to the Le Cam methodology usually reserved for linearmultivariate analysis. We construct locally and asymptotically most stringent parametric testsfor ANOVA for directional data within the class of rotationally symmetric distributions. We turnthese parametric tests into semi-parametric ones by (i) using a studentization argument (whichleads to what we call pseudo-FvML tests) and by (ii) resorting to the invariance principle (whichleads to e_cient rank-based tests). Within each construction the semi-parametric tests inheritoptimality under a given distribution (the FvML distribution in the _rst case, any rotationallysymmetric distribution in the second) from their parametric antecedents and also improve onthe latter by being valid under the whole class of rotationally symmetric distributions. Asymp-totic relative e_ciencies are calculated and the _nite-sample behavior of the proposed tests isinvestigated by means of a Monte Carlo simulation. We conclude by applying our _ndings on areal-data example involving geological data.