基于范数的失真度量下概率分布的量化

Statistics & Decisions Pub Date : 2004-04-01 DOI:10.1524/stnd.22.4.261.64314

S. Delattre, S. Graf, H. Luschgy, G. Pagès

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引用次数: 36

摘要

对于在Rd和n * n上的概率测度P，考虑en = in∫mina * αV(||x−a||)dP(x)，其中最小值取于Rd的所有子集α，且card(α)≤n，且V是一个非递减函数。在V上的一定条件下，我们导出了非奇异分布P的精确n渐近性，并利用加权经验测度找到了最优量化器的渐近性能。

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Quantization of probability distributions under norm-based distortion measures

Summury 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.

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Statistics & Decisions

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