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Gaussian limits for generalized spacings


Reference:

Baryshnikov, Y., Penrose, M. D. and Yukich, J. E., 2009. Gaussian limits for generalized spacings. Annals of Applied Probability, 19 (1), pp. 158-185.

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http://projecteuclid.org/euclid.aoap/1235140336

Abstract

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.

Details

Item Type Articles
CreatorsBaryshnikov, Y., Penrose, M. D. and Yukich, J. E.
DOI10.1214/08-aap537
Uncontrolled Keywordsφ-divergence, logarithmic spacings, log-likelihood, central limit theorems, spacing statistics, information gain
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code13846

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