Manifold estimation and singular deconvolution under Hausdorff loss

Abstract

We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.

Published in at http://dx.doi.org/10.1214/12-AOS994 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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