The Annals of Statistics

Manifold estimation and singular deconvolution under Hausdorff loss

Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, and Larry Wasserman

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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.

Article information

Source
Ann. Statist. Volume 40, Number 2 (2012), 941-963.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.aos/1338515143

Digital Object Identifier
doi:10.1214/12-AOS994

Mathematical Reviews number (MathSciNet)
MR2985939

Zentralblatt MATH identifier
1274.62237

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62H12: Estimation

Keywords
Deconvolution manifold learning minimax

Citation

Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry. Manifold estimation and singular deconvolution under Hausdorff loss. Ann. Statist. 40 (2012), no. 2, 941--963. doi:10.1214/12-AOS994. http://projecteuclid.org/euclid.aos/1338515143.


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