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November 2018 Methods for Estimation of Convex Sets
Victor-Emmanuel Brunel
Statist. Sci. 33(4): 615-632 (November 2018). DOI: 10.1214/18-STS669

Abstract

In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming, extreme value theory, etc. The statistical problems that we review include density support estimation, estimation of the level sets of densities or depth functions, nonparametric regression, etc. We focus on the estimation of convex sets under the Nikodym and Hausdorff metrics, which require different techniques and, quite surprisingly, lead to very different results, in particular in density support estimation. Finally, we discuss computational issues in high dimensions.

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Victor-Emmanuel Brunel. "Methods for Estimation of Convex Sets." Statist. Sci. 33 (4) 615 - 632, November 2018. https://doi.org/10.1214/18-STS669

Information

Published: November 2018
First available in Project Euclid: 29 November 2018

zbMATH: 07032832
MathSciNet: MR3881211
Digital Object Identifier: 10.1214/18-STS669

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.33 • No. 4 • November 2018
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