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2013 Fast rates for empirical vector quantization
Clément Levrard
Electron. J. Statist. 7(none): 1716-1746 (2013). DOI: 10.1214/13-EJS822

Abstract

We consider the rate of convergence of the expected loss of empirically optimal vector quantizers. Earlier results show that the mean-squared expected distortion for any fixed probability distribution supported on a bounded set and satisfying some regularity conditions decreases at the rate $\mathcal{O}(\log n/n)$. We prove that this rate is actually $\mathcal{O}(1/n)$. Although these conditions are hard to check, we show that well-clustered distributions with continuous densities supported on a bounded set are included in the scope of this result.

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Clément Levrard. "Fast rates for empirical vector quantization." Electron. J. Statist. 7 1716 - 1746, 2013. https://doi.org/10.1214/13-EJS822

Information

Published: 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1349.62038
MathSciNet: MR3080408
Digital Object Identifier: 10.1214/13-EJS822

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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