Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles Quantization of probability distributions under norm-based distortion measures. (English) Zbl 1066.60026 Stat. Decis. 22, No. 4, 261-282 (2004). Summary: For a probability measure \(P\) on \(\mathbb{R}^d\) and \(n\in \mathbb{N}\) consider \(e_n=\inf\int\min_{a\in\alpha}V(\|x-a\|)dP(x)\) where the infimum is taken over all subsets \(\alpha\) of \(\mathbb{R}^d\) with \(\text{card}(\alpha)\leq n\) 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. Cited in 1 ReviewCited in 18 Documents MSC: 60E99 Distribution theory 94A29 Source coding 28A80 Fractals Keywords:high-rate vector quantization; norm-difference distortion; empirical measure; weak convergence; local distortion; point density measure PDFBibTeX XMLCite \textit{S. Delattre} et al., Stat. Decis. 22, No. 4, 261--282 (2004; Zbl 1066.60026) Full Text: DOI HAL