par Ley, Christophe ;Swan, Yvik ;Thiam, Baba;Verdebout, Thomas
Référence Statistica sinica, 23, page (305-332)
Publication Publié, 2013
Article révisé par les pairs
Résumé : In this paper, we provide R-estimators of the location of a rotationally symmetric distribution on the unit sphere of Rk. 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.