Abstract
In This Article, the Moments of Nearest Neighbor Distance Distributions Are 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 More 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 Rényi Entropies of Probability Distributions. Moreover, the Algebraic Technique Developed May Turn Out to Be Useful in Other, Related Problems Including Estimation of the Shannon Differential Entropy. © 2010 Wiley Periodicals, Inc.
Recommended Citation
E. Liitiäinen et al., "A Boundary Corrected Expansion of the Moments of Nearest Neighbor Distributions," Random Structures and Algorithms, vol. 37, no. 2, pp. 223 - 247, Wiley, Sep 2010.
The definitive version is available at https://doi.org/10.1002/rsa.20311
Department(s)
Engineering Management and Systems Engineering
Publication Status
Full Access
Keywords and Phrases
Boundary; Edge; Moments; Nearest neighbor; Random geometry
International Standard Serial Number (ISSN)
1098-2418; 1042-9832
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Wiley, All rights reserved.
Publication Date
01 Sep 2010
