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.
Manifold estimation and singular deconvolution under Hausdorff loss / Genovese, Christopher R.; Perone Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - 40:2(2012), pp. 941-963. [10.1214/12-aos994]
Manifold estimation and singular deconvolution under Hausdorff loss
Marco Perone Pacifico;
2012
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.
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