GAUSSIAN LIMITS FOR GENERALIZED SPACINGS

• 成果类型: Article
• 署名作者: Baryshnikov, Yu.; Penrose, Mathew D.; Yukichi, J. E.
• 署名单位: Alcatel-Lucent; Lucent Technologies; AT&T; University of Bath; Lehigh University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP537
• 发表日期: 2009
• 页码: 158-185
• 关键词: sample spacings; sum-functions; k-spacings; GOODNESS; tests; association; statistics; logarithms; dispersion; distances

摘要

Nearest neighbor cells in R-d, d is an element of N, are used to define coefficients of divergence (phi-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.