The Annals of Statistics

Optimal rates of convergence for convex set estimation from support functions

Adityanand Guntuboyina

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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.

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

First available in Project Euclid: 16 April 2012

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Zentralblatt MATH identifier

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

Convex set estimation support function least squares regularization optimal minimax rates


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.

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