DETECTION OF CORRELATIONS

• 成果类型: Article
• 署名作者: Arias-Castro, Ery; Bubeck, Sebastien; Lugosi, Gabor
• 署名单位: University of California System; University of California San Diego; Princeton University; Pompeu Fabra University; ICREA
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS964
• 发表日期: 2012
• 页码: 412-435
• 关键词: higher criticism; random-fields; rates

摘要

We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of possibly correlated sets. We show that some simple tests have near-optimal performance in many cases, while the generalized likelihood ratio test is suboptimal in some important cases.