Quantization of probability distributions under norm-based distortion measures

Delattre Sylvain, Graf Siegfried, Luschgy Harald and Pagès Gilles

Statistics & Risk Modeling, 2004, vol. 22, issue 4, 261-282

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

Date: 2004
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DOI: 10.1524/stnd.22.4.261.64314

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