Strong consistency of \(K\)-centres in reflexive spaces (Q2769692)

The idea of approximation of a random variable by \(k\) points leads to a notion of the \(k\)-centre of probability distributions [see \textit{D. Pollard}, Ann. Stat. 9, 135-140 (1981; Zbl 0451.62048)]. Some best approximation theory results combined with the Skorohod representation theorem are used for proving the strong consistency in Hausdorff metrics of sample-based \(k\)-centres for a wide class of distributions in reflexive spaces. The consistency of empirical minimal distances and Voronoi regions is considered as well.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].