Manifold estimation and singular deconvolution under Hausdorff loss
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry H. Wasserman · 2011
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.