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April 2012 Manifold estimation and singular deconvolution under Hausdorff loss
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman
Ann. Statist. 40(2): 941-963 (April 2012). DOI: 10.1214/12-AOS994

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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Christopher R. Genovese. Marco Perone-Pacifico. Isabella Verdinelli. Larry Wasserman. "Manifold estimation and singular deconvolution under Hausdorff loss." Ann. Statist. 40 (2) 941 - 963, April 2012. https://doi.org/10.1214/12-AOS994

Information

Published: April 2012
First available in Project Euclid: 1 June 2012

zbMATH: 1274.62237
MathSciNet: MR2985939
Digital Object Identifier: 10.1214/12-AOS994

Subjects:
Primary: 62G05 , 62G20
Secondary: 62H12

Keywords: Deconvolution , manifold learning , minimax

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 2 • April 2012
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