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Constructive quadratic functional quantization and critical dimension


 
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1. Title Title of document Constructive quadratic functional quantization and critical dimension
 
2. Creator Author's name, affiliation, country Harald Luschgy; Universität Trier; Germany
 
2. Creator Author's name, affiliation, country Gilles Pagès; Université Paris 6 UPMC; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) quadratic functional quantization; Karhunen-Lo\`eve expansion; Gaussian process ; optimal quantizer ; asymptotically optimal quantizer ; Shannon's entropy
 
3. Subject Subject classification 60G15 ; 60G99 ; 94A29
 
4. Description 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). 
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-06-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3010
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3010
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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