POISSON APPROXIMATION FOR TWO SCAN STATISTICS WITH RATES OF CONVERGENCE

• 成果类型: Article
• 署名作者: Fang, Xiao; Siegmund, David
• 署名单位: National University of Singapore; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1150
• 发表日期: 2016
• 页码: 2384-2418
• 关键词: tail probabilities; SEQUENCES

摘要

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.