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Title: Properties of estimators of the quantization dimension of distributions Authors:  Klaus Poetzelberger - WU Vienna (Austria) [presenting]
Abstract: Estimators of the dimension of the support of a probability distribution are presented. These estimators are derived from the concept of quantization dimension. For the general case consistency results are discussed. Versions of the estimators may be applied for instance to estimate the dimension of the driving Brownian motion of Ito processes or the dimension of the attractor of a dynamical system. A second application of estimators of dimension is the analysis of high-dimensional data $X$ where the stochastic properties of $X$ are explained by a vector of factors $W$ in the sense that for a sufficiently smooth (Lipschitz) mapping $f$, $X=f(W)$ and $s:=\mbox{dim}(W)<<\mbox{dim}(X)=:d$. We focus on regularity conditions that imply the consistency of the estimators, on numerical experiments to check the performance of the estimators and on the choice of the norm for the quantization.