Optimal rates of convergence for convex set estimation from support functions

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.

Published in at http://dx.doi.org/10.1214/11-AOS959 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Convergence of algorithms for reconstructing convex bodies and directional measures
• Nonparametric estimation of multivariate convex-transformed densities
• Recovering convex boundaries from blurred and noisy observations

Cited by in corpus (1)

• Fitting Tractable Convex Sets to Support Function Evaluations