Sequential selection of an increasing sequence from a multidimensional random sample

• 成果类型: Article
• 署名作者: Baryshnikov, YM; Gnedin, AV
• 署名单位: Eindhoven University of Technology; University of Gottingen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1019737672
• 发表日期: 2000
• 页码: 258-267
• 关键词: records

摘要

Let random points X-1,...,X-n be sampled in strict sequence from a continuous product distribution on Euclidean d-space. At the time X-j is observed it must be accepted or rejected. The subsequence of accepted points must increase in each coordinate. We show that the maximum expected length of a subsequence selected is asymptotic to gamman(1/(d+1)) and give the exact value of gamma. This extends the root 2n result by Samuels and Steele for d = 1.