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arXiv · 1109.4962

Optimal R-Estimation of a Spherical Location

Christophe Ley·Yvik Swan·Baba Thiam·Thomas Verdebout
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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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Christophe Ley, Yvik Swan, Baba Thiam, Thomas Verdebout. 2012-03-27. Optimal R-Estimation of a Spherical Location. https://arxiv.org/abs/1109.4962

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