Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions

For a probability measure P on Rd and n ∈ N consider en = inf mina∈α V ( x − a )dP(x) where the infimum is taken over all subsets α of Rd with card(α) n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n-asymptotics of en for self-similar distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.  2005 Elsevier Inc. All rights reserved