Quantization of probability distributions under norm-based distortion measures

Abstract

Summury For a probability measure P on Rd and n ∊ N consider en = inf ∫ mina∊αV(||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 nonsingular distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.