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Baryshnikov, Yu.; Penrose, Mathew D.; Yukich, J. E.

Gaussian limits for generalized spacings. (English) Zbl 1159.60315

Ann. Appl. Probab. 19, No. 1, 158-185 (2009).
Summary: Nearest neighbor cells in \(\mathbb{R}^d, d\in \mathbb N\), 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.

Cited in 20 Documents

MSC:

60F05 Central limit and other weak theorems
60D05 Geometric probability and stochastic geometry
62H11 Directional data; spatial statistics

Keywords:

\(\phi \)-divergence; central limit theorems; spacing statistics; logarithmic spacings; information gain; log-likelihood
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References:

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