Gaussian limits for generalized spacings

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

Research output: Contribution to journalArticlepeer-review

Abstract

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 (US)
Pages (from-to)158-185
Number of pages28
JournalAnnals of Applied Probability
Volume19
Issue number1
DOIs
StatePublished - Feb 2009
Externally publishedYes

Keywords

  • Central limit theorems
  • Information gain
  • Log-likelihood
  • Logarithmic spacings
  • Oslash;-Divergence
  • Spacing statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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