The Annals of Statistics

Optimal rates of convergence for convex set estimation from support functions

Adityanand Guntuboyina

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Abstract

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.

Article information

Source
Ann. Statist., Volume 40, Number 1 (2012), 385-411.

Dates
First available in Project Euclid: 16 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1334581747

Digital Object Identifier
doi:10.1214/11-AOS959

Mathematical Reviews number (MathSciNet)
MR3014311

Zentralblatt MATH identifier
1246.62085

Subjects
Primary: 62G08: Nonparametric regression 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

Keywords
Convex set estimation support function least squares regularization optimal minimax rates

Citation

Guntuboyina, Adityanand. Optimal rates of convergence for convex set estimation from support functions. Ann. Statist. 40 (2012), no. 1, 385--411. doi:10.1214/11-AOS959. https://projecteuclid.org/euclid.aos/1334581747


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