LAUSR

Abstract Recently, Verdebout (2015) introduced a Kruskal–Wallis type rank-based procedure ϕ V ( n ) to test the homogeneity of concentrations of some distributions on the unit hypersphere S p − 1 of R p . While the asymptotic properties of ϕ V ( n ) are known under the null hypothesis, nothing is known about its behavior under local alternatives. In this paper we compute the asymptotic relative efficiency of ϕ V ( n ) with respect to the optimal Fisher–von Mises (FvM) score test ϕ WJ ( n ) of Watamori and Jupp (2005) in the FvM case. Quite surprisingly we obtain that in the vicinity of the uniform distribution of S 2 , ϕ V ( n ) and ϕ WJ ( n ) do perform almost equally well. This implies that the natural robustness of ϕ V ( n ) that comes from the use of ranks has no asymptotic efficiency cost in the vicinity of the 3 -dimensional uniform distribution.