Bounds on the power-weighted mean nearest neighbor distance
Elia Liitiäinen, Amaury Lendasse and Francesco Corona
Proceedings of the Royal Society, Series A
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.