Quantization of probability distributions under norm-based distortion measures

Summury For a probability measure P on R d and n ∊ N consider e n = inf ∫ min a∊α V (|| x − a ||) dP ( x ) where the infimum is taken over all subsets α of R d with card(α) ≤ n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n -asymptotics of e n for nonsingular distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.

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Year of publication:	2004
Authors:	Delattre, Sylvain ; Graf, Siegfried ; Luschgy, Harald ; Pagès, Gilles
Published in:	Statistics & Decisions. - Oldenbourg Wissenschaftsverlag GmbH, ISSN 2196-7040, ZDB-ID 2630803-4. - Vol. 22.2004, 4, p. 261-282
Publisher:	Oldenbourg Wissenschaftsverlag GmbH

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Type of publication:	Article
Language:	Undetermined
Other identifiers:	10.1524/stnd.22.4.261.64314 [DOI]
Source:	Other ZBW resources

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