GLOBAL TESTING AGAINST SPARSE ALTERNATIVES UNDER ISING MODELS

• 成果类型: Article
• 署名作者: Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
• 署名单位: University of California System; University of California Berkeley; Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1612
• 发表日期: 2018
• 页码: 2062-2093
• 关键词: higher criticism; detection boundary; steins method; statistics

摘要

In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie-Weiss model where we observe the effect of a thermodynamic phase transition. In particular, the critical state exhibits a subtle blessing of dependence phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax optimal under fairly general regularity conditions.