A Boundary Corrected Expansion of the Moments of Nearest Neighbor Distributions

作者：Liitiainen Elia^*; Lendasse Amaury; Corona Francesco

来源：Random Structures and Algorithms, 2010, 37(2): 223-247.

DOI：10.1002/rsa.20311

• nearest neighbor
• moments
• boundary
• edge
• random geometry

In this article, the moments of nearest neighbor distance distributions ate examined While the asymptotic form of such moments is well-known. the boundary effect has this far resisted a rigorous analysis Our goal is to develop a new technique that allows a closed-form high order expansion, where the boundaries are taken into account up to the first order The resulting theoretical predictions are tested via simulations and found to be much mole accurate than the first order approximation obtained by neglecting the boundaries
While our results are of theoretical interest, they definitely also have important applications in Statistics and physics As a concrete example, we mention estimating Renyi entropies of probability distributions Moreover. the algebr

• 出版日期2010-9