Gaussian limits for generalized spacings

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

Research output: Contribution to journalArticle

20 Citations (Scopus)

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
Pages (from-to)158-185
Number of pages28
JournalAnnals of Applied Probability
Volume19
Issue number1
DOIs
Publication statusPublished - Feb 1 2009

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Spacing
Log-likelihood Ratio
Information Gain
Sample point
Central limit theorem
Nearest Neighbor
Divergence
Logarithmic
Sample Size
Cell
Coefficient
Sample size
Likelihood ratio
Coefficients
Nearest neighbor

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Baryshnikov, Y., Penrose, M. D., & Yukich, J. E. (2009). Gaussian limits for generalized spacings. Annals of Applied Probability, 19(1), 158-185. https://doi.org/10.1214/08-AAP537

Gaussian limits for generalized spacings. / Baryshnikov, Yu; Penrose, Mathew D.; Yukich, J. E.

In: Annals of Applied Probability, Vol. 19, No. 1, 01.02.2009, p. 158-185.

Research output: Contribution to journalArticle

Baryshnikov, Y, Penrose, MD & Yukich, JE 2009, 'Gaussian limits for generalized spacings', Annals of Applied Probability, vol. 19, no. 1, pp. 158-185. https://doi.org/10.1214/08-AAP537
Baryshnikov Y, Penrose MD, Yukich JE. Gaussian limits for generalized spacings. Annals of Applied Probability. 2009 Feb 1;19(1):158-185. https://doi.org/10.1214/08-AAP537
Baryshnikov, Yu ; Penrose, Mathew D. ; Yukich, J. E. / Gaussian limits for generalized spacings. In: Annals of Applied Probability. 2009 ; Vol. 19, No. 1. pp. 158-185.
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