Gaussian limits for generalized spacings

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

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


Nearest neighbor cells in R d,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 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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