Gaussian limits for generalized spacings

Abstract

Nearest neighbor cells in $R^d,d\in \mathbb{N}$, are used to define coefficients of divergence ($\varphi$-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.

Published in at http://dx.doi.org/10.1214/08-AAP537 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Gaussian limits for random measures in geometric probability
• Laws of large numbers in stochastic geometry with statistical applications
• Gaussian limits for generalized spacings

Cited by in corpus (1)

• Gaussian limits for generalized spacings