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

Overview & Synopsis

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.