Universal -rate-optimality of -optimal quantizers by dilatation and contraction

Abstract : We investigate in this paper the properties of some dilatations or contractions of a sequence of -optimal quantizers of an -valued random vector defined in the probability space with distribution . To be precise, we investigate the -quantization rate of sequences when or and . We show that for a wide family of distributions, one may always find parameters such that is -rate-optimal. For the Gaussian and the exponential distributions we show the existence of a couple such that also satisfies the so-called -empirical measure theorem. Our conjecture, confirmed by numerical experiments, is that such sequences are asymptotically -optimal. In both cases the sequence is incredibly close to -optimality. However we show (see Rem. 5.4) that this last sequence is not -optimal ( when = 2,  = 1) for the exponential distribution.
Keywords : Mathematics
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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.218-246. 〈10.1051/ps:2008008〉
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Abass Sagna. Universal -rate-optimality of -optimal quantizers by dilatation and contraction. ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.218-246. 〈10.1051/ps:2008008〉. 〈hal-00491506〉

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