Gaussian limits for generalized spacings

Y Baryshnikov, Mathew D Penrose, J E Yukich

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23 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)158-185
Number of pages28
JournalAnnals of Applied Probability
Issue number1
Publication statusPublished - Feb 2009


  • φ-divergence
  • logarithmic spacings
  • log-likelihood
  • central limit theorems
  • spacing statistics
  • information gain


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