  In this paper, we provide $R$-estimators of the location of a rotationally
symmetric distribution on the unit sphere of $\R^k$. In order to do so we first
prove the local asymptotic normality property of a sequence of rotationally
symmetric models; this is a non standard result due to the curved nature of the
unit sphere. We then construct our estimators by adapting the Le Cam one-step
methodology to spherical statistics and ranks. We show that they are
asymptotically normal under any rotationally symmetric distribution and achieve
the efficiency bound under a specific density. Their small sample behavior is
studied via a Monte Carlo simulation and our methodology is illustrated on
geological data.
