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This article is cited in 8 scientific papers (total in 8 papers)
Quantization for Probability Measures in the Prokhorov Metric
S. Graf, H. Luschgy University of Passau
Abstract:
For a probability distribution $P$ on $R^d$ and $n\inN$ consider $e_n=\inf\pi(P,Q)$, where $\pi$ denotes the Prokhorov metric and the infimum is taken over all discrete probabilities $Q$ with $|\mathrm{supp}(Q)|\le n$. We study solutions $Q$ of this minimization problem, stability properties, and consistency of empirical estimators. For some classes of distributions we determine the exact rate of convergence to zero of the $n$th quantization error $e_n$ as $n\to\infty$.
Keywords:
multidimensional quantization, Ky Fan metric, Prokhorov metric, optimal quantizers, empirical measures, asymptotic quantization error, entropy, quantization dimension.
Received: 25.11.2003 Revised: 22.05.2007
Citation:
S. Graf, H. Luschgy, “Quantization for Probability Measures in the Prokhorov Metric”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 307–335; Theory Probab. Appl., 53:2 (2009), 216–241
Linking options:
https://www.mathnet.ru/eng/tvp2411https://doi.org/10.4213/tvp2411 https://www.mathnet.ru/eng/tvp/v53/i2/p307
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