Electronic Journal of Statistics

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

Antoine Godichon-Baggioni and Bruno Portier

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 1890-1927.

Dates
Received: February 2016
First available in Project Euclid: 3 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1493776837

Digital Object Identifier
doi:10.1214/17-EJS1276

Mathematical Reviews number (MathSciNet)
MR3645879

Zentralblatt MATH identifier
06715792

Keywords
Projected Robbins-Monro algorithm sphere fitting averaging asymptotic properties

Rights
Creative Commons Attribution 4.0 International License.

Citation

Godichon-Baggioni, Antoine; Portier, Bruno. An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution. Electron. J. Statist. 11 (2017), no. 1, 1890--1927. doi:10.1214/17-EJS1276. https://projecteuclid.org/euclid.ejs/1493776837


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