The local quantization behaviour of absolutely continuous probabilities

Details The local quantization behaviour of absolutely continuous probabilities The local quantization behaviour of absolutely continuous probabilities

2010-09-26

arxiv.org/abs/1009.5093v1

Mathematics

Probability

35p

Scientific paper

For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L^r(P)-codebooks \alpha_n, and any Voronoi partition V_{n,a} with respect to \alpha_n the local probabilities P(V_{n,a}) satisfy P(V_{a,n}) \approx n^{-1} while the local L^r-quantization errors satisfy $\int_{V_{n,a}} \|x-a\|^r dP(x) \approx n^{- (1+ \frac rd)}$ as long as the partition sets V_{n,a} intersect a fixed compact set K in the interior of the support of P.

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