Open Access
Translator Disclaimer
February 2012 Optimal rates of convergence for convex set estimation from support functions
Adityanand Guntuboyina
Ann. Statist. 40(1): 385-411 (February 2012). DOI: 10.1214/11-AOS959

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.

Citation

Download Citation

Adityanand Guntuboyina. "Optimal rates of convergence for convex set estimation from support functions." Ann. Statist. 40 (1) 385 - 411, February 2012. https://doi.org/10.1214/11-AOS959

Information

Published: February 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1246.62085
MathSciNet: MR3014311
Digital Object Identifier: 10.1214/11-AOS959

Subjects:
Primary: 52A20 , 62G08

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

Rights: Copyright © 2012 Institute of Mathematical Statistics

JOURNAL ARTICLE
27 PAGES


SHARE
Vol.40 • No. 1 • February 2012
Back to Top