Gaussian limits for generalized spacings

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Nearest neighbor cells in $R^d,d\in\mathbb{N}$, 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.
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)

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Probability, Statistics Theory, 60F05, 60D05, 62H11 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/222301

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.4123
 http://arxiv.org/abs/0804.4123
 Annals of Applied Probability 2009, Vol. 19, No. 1, 158-185
 doi:10.1214/08-AAP537

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arXiv