Bounds on the mean power-weighted nearest neighbour distance
Elia Liitiäinen, Amaury Lendasse, Francesco Corona · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2008
In this paper, bounds on the mean power-weighted nearest neighbour distance are derived. Previous work concentrates mainly on the infinite sample limit, whereas our bounds hold for any sample size. The results are expected to be of importance, for example in statistical physics, non-parametric statistics and computational geometry, where they are related to the structure of matter as well as properties of statistical estimators and random graphs.