Open Access
August 2016 Global testing against sparse alternatives in time-frequency analysis
T. Tony Cai, Yonina C. Eldar, Xiaodong Li
Ann. Statist. 44(4): 1438-1466 (August 2016). DOI: 10.1214/15-AOS1412


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.


Download Citation

T. Tony Cai. Yonina C. Eldar. Xiaodong Li. "Global testing against sparse alternatives in time-frequency analysis." Ann. Statist. 44 (4) 1438 - 1466, August 2016.


Received: 1 June 2015; Revised: 1 October 2015; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1359.62032
MathSciNet: MR3519929
Digital Object Identifier: 10.1214/15-AOS1412

Primary: 62C20 , 62F03 , 62F05 , 62G30 , 62G32

Keywords: Detection boundary , Empirical processes , higher criticism , over-sampled periodogram , Sparsity , Testing for periodicity

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
Back to Top