## Electronic Journal of Statistics

### Fast rates for empirical vector quantization

Clément Levrard

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 7 (2013), 1716-1746.

Dates
First available in Project Euclid: 3 July 2013

https://projecteuclid.org/euclid.ejs/1372861686

Digital Object Identifier
doi:10.1214/13-EJS822

Mathematical Reviews number (MathSciNet)
MR3080408

Zentralblatt MATH identifier
1349.62038

#### Citation

Levrard, Clément. Fast rates for empirical vector quantization. Electron. J. Statist. 7 (2013), 1716--1746. doi:10.1214/13-EJS822. https://projecteuclid.org/euclid.ejs/1372861686

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