Nearest neighbor cells in Rd, d∈ℕ, are used to define coefficients of divergence (φ-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.
Publié le : 2009-02-15
Classification:
φ-divergence,
central limit theorems,
spacing statistics,
logarithmic spacings,
information gain,
log-likelihood,
60F05,
60D05,
62H11
@article{1235140336,
author = {Baryshnikov, Yu. and Penrose, Mathew D. and Yukich, J. E.},
title = {Gaussian limits for generalized spacings},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 158-185},
language = {en},
url = {http://dml.mathdoc.fr/item/1235140336}
}
Baryshnikov, Yu.; Penrose, Mathew D.; Yukich, J. E. Gaussian limits for generalized spacings. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 158-185. http://gdmltest.u-ga.fr/item/1235140336/