An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution

Abstract : The objective of this work is to propose a new algorithm to fit a sphere on a noisy 3D point cloud distributed around a complete or a truncated sphere. More precisely, we introduce a projected Robbins-Monro algorithm and its averaged version for estimating the center and the radius of the sphere. We give asymptotic results such as the almost sure convergence of these algorithms as well as the asymptotic normality of the averaged algorithm. Furthermore, some non-asymptotic results will be given, such as the rates of convergence in quadratic mean. Some numerical experiments show the efficiency of the proposed algorithm on simulated data for small to moderate sample sizes and for modeling an object in 3D.
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https://hal.archives-ouvertes.fr/hal-01591601
Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, September 21, 2017 - 3:48:24 PM
Last modification on : Thursday, February 7, 2019 - 2:25:28 PM

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Antoine Godichon, Bruno Portier. An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2017, 11 (1), pp.1890 - 1927. ⟨10.1214/17-EJS1276⟩. ⟨hal-01591601⟩

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