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Mathematics > Statistics Theory

arXiv:1410.6966 (math)
[Submitted on 25 Oct 2014 (v1), last revised 27 Sep 2016 (this version, v2)]

Title:Global testing against sparse alternatives in time-frequency analysis

Authors:T. Tony Cai, Yonina C. Eldar, Xiaodong Li
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Abstract: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.
Comments: Published at this http URL in the Annals of Statistics (this http URL) by the Institute of Mathematical Statistics (this http URL)
Subjects: Statistics Theory (math.ST)
Report number: IMS-AOS-AOS1412
Cite as: arXiv:1410.6966 [math.ST]
  (or arXiv:1410.6966v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.1410.6966
Journal reference: Annals of Statistics 2016, Vol. 44, No. 4, 1438-1466
Related DOI: https://doi.org/10.1214/15-AOS1412

Submission history

From: T. Tony Cai [view email] [via VTEX proxy]
[v1] Sat, 25 Oct 2014 22:21:17 UTC (107 KB)
[v2] Tue, 27 Sep 2016 12:51:54 UTC (346 KB)
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