GLOBAL TESTING AGAINST SPARSE ALTERNATIVES IN TIME-FREQUENCY ANALYSIS

• 成果类型: Article
• 署名作者: Cai, T. Tony; Eldar, Yonina C.; Li, Xiaodong
• 署名单位: University of Pennsylvania; Technion Israel Institute of Technology; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1412
• 发表日期: 2016
• 页码: 1438-1466
• 关键词: higher criticism; sinusoids; parameter

摘要

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by O(log N) is proven universally optimal in global testing for periodicities under a mild minimum separation condition.