Electronic Journal of Statistics

Tight minimax rates for manifold estimation under Hausdorff loss

Arlene K. H. Kim and Harrison H. Zhou

Full-text: Open access

Abstract

This paper deals with minimax rates of convergence for manifold estimation. A new lower bound is obtained by a novel construction of two sets of manifolds and an application of convex hull testing method of Le Cam (1973). The minimax lower bound matches the upper bound up to a constant factor considered by Genovese et al. (2012b).

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 1562-1582.

Dates
Received: November 2013
First available in Project Euclid: 23 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1437658703

Digital Object Identifier
doi:10.1214/15-EJS1039

Mathematical Reviews number (MathSciNet)
MR3376117

Zentralblatt MATH identifier
1325.62111

Subjects
Primary: 62C25: Compound decision problems 62G86: Nonparametric inference and fuzziness
Secondary: 65C50: Other computational problems in probability

Keywords
minimax lower bound manifold estimation convex hull testing

Citation

Kim, Arlene K. H.; Zhou, Harrison H. Tight minimax rates for manifold estimation under Hausdorff loss. Electron. J. Statist. 9 (2015), no. 1, 1562--1582. doi:10.1214/15-EJS1039. https://projecteuclid.org/euclid.ejs/1437658703


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