Optimal R-Estimation of a Spherical Location

2011/09/22 by Christophe Ley, Ley, Christophe, Yvik Swan +5
Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #stat.AP

paper · pdf · doi:10.48550/arxiv.1109.4962

Accepted in Statistica Sinica

arxiv created 2012/03/27 · arxiv updated 2012/03/28

Abstract

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.

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