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2014 Constructive quadratic functional quantization and critical dimension
Harald Luschgy, Gilles Pagès
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Electron. J. Probab. 19: 1-19 (2014). DOI: 10.1214/EJP.v19-3010

Abstract

We propose a constructive proof for the sharp rate of optimal quadratic functional quantization and we tackle the asymptotics of the critical dimension for quadratic functional quantization of Gaussian stochastic processes as the quantization level goes to infinity, i.e. the smallest dimensional truncation of an optimal quantization of the process which is "fully" quantized. We first establish a lower bound for this critical dimension based on the regular variation index of the eigenvalues of the Karhunen-Loève expansion of the process. This lower bound is consistent with the commonly shared sharp rate conjecture (and supported by extensive numerical experiments). Moreover, we show that, conversely, optimized quadratic functional quantizations based on this critical dimension rate are always asymptotically optimal (strong admissibility result).

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Harald Luschgy. Gilles Pagès. "Constructive quadratic functional quantization and critical dimension." Electron. J. Probab. 19 1 - 19, 2014. https://doi.org/10.1214/EJP.v19-3010

Information

Accepted: 13 June 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1348.60056
MathSciNet: MR3227059
Digital Object Identifier: 10.1214/EJP.v19-3010

Subjects:
Primary: 60G15
Secondary: 60G99 , 94A29

Keywords: asymptotically optimal quantizer , Gaussian process , Karhunen-Lo\`eve expansion , optimal quantizer , quadratic functional quantization , Shannon's entropy

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