arXiv subjects

Siegried Graf

Publications and source records attributed to Siegried Graf.

2 recordsLinked to original sources

arXiv2006

Distortion mismatch in the quantization of probability measures

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.

math.PR↗

arXiv2005

Optimal quantizers for Radon random vectors in a Banach space

For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\_{n,r}(X,E) = inf{(E (\min\_{a \in α} || X-a ||^r)^{1/r}}, where the infimum is taken over all subsets αof E with card(α) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.

math.PR↗