S. Graf

activity

20052010

most citedThe local quantization behavior of absolutely continuous probabilities

28 citations · 29 across the 3 of their papers we have counts for

collaborators

3 papers

math.PR2010★ 28 cited

The local quantization behavior of absolutely continuous probabilities

Siegfried Graf, Harald Luschgy, Gilles Pagès

For a large class of absolutely continuous probabilities $P$ it is shown that, for $r > 0$ , for $n$ -optimal $L^{r} (P)$ -codebooks $α_{n}$ , and any Voronoi partition $V_{n, a}$ with respect…

math.PR2006

Distortion mismatch in the quantization of probability measures

Siegried Graf, Harald Luschgy, Gilles Pagès

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…

math.PR2005★ 1 cited

Optimal quantizers for Radon random vectors in a Banach space

Siegried Graf, Harald Luschgy, Pagès Gilles

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…