We show that results on the characterization of admissible quantizations, which have been derived in Potzelberger [3], have to be modified in case the probability distribution has linear components. Furthermore, we provide an example, where the limit of optimal quantizations is not admissible. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Let P be a Borel probability measure on Rd. We characterize the maximal elements p E M(P,m) with respect to the Bishop-De Leeuw order, where p E M(P, m) if and only if p P and [supp(p)] m. The results obtained have important consequences for statistical inference, such as tests of homogeneity or multivariate cluster analysis and for the theory of comparison of experiments. (author's abstract) / Series: Forschungsberichte / Institut für Statistik