%0 Journal Article
%T Gaussian limits for generalized spacings
%A Yu. Baryshnikov
%A Mathew D. Penrose
%A J. E. Yukich
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/08-AAP537
%X Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a variance depending on the underlying point density. In $d=1$, this extends classical central limit theory for sum functions of spacings. The general results yield central limit theorems for logarithmic $k$-spacings, information gain, log-likelihood ratios and the number of pairs of sample points within a fixed distance of each other.
%U http://arxiv.org/abs/0804.4123v2