2 research outputs found
Constructive quantization: approximation by empirical measures
In this article, we study the approximation of a probability measure on
by its empirical measure interpreted as a
random quantization. As error criterion we consider an averaged -th moment
Wasserstein metric. In the case where , we establish refined upper and
lower bounds for the error, a high-resolution formula. Moreover, we provide a
universal estimate based on moments, a so-called Pierce type estimate. In
particular, we show that quantization by empirical measures is of optimal order
under weak assumptions.Comment: 22 page