ASYMPTOTIC DISTRIBUTION OF THE MAXIMUM INTERPOINT DISTANCE IN A SAMPLE OF RANDOM VECTORS WITH A SPHERICALLY SYMMETRIC DISTRIBUTION

• 成果类型: Article
• 署名作者: Jammalamadaka, Sreenivasa Rao; Janson, Svante
• 署名单位: University of California System; University of California Santa Barbara; Uppsala University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1082
• 发表日期: 2015
• 页码: 3571-3591
• 关键词: random point set; statistics

摘要

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum interpoint distance,'' in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complements our earlier study on the minimum interpoint distance.