Distortion mismatch in the quantization of probability measures

Research paper by Siegried Graf, Harald Luschgy, Gilles Pagès

Indexed on: 17 Feb '06Published on: 17 Feb '06Published in: Mathematics - Probability


We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s<r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based quadrature formulae in numerical integration on R^d and on the Wiener space.