Cai, TonyEldar, Yonina CLi, Xiaodong2023-05-232023-05-232016-01-012017-08-22https://repository.upenn.edu/handle/20.500.14332/48078In 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 conditionThe original and published work is available at: https://projecteuclid.org/euclid.aos/1467894704Testing for periodicitysparsityover-sampled periodogramhigher criticismdetection boundaryempirical processesPhysical Sciences and MathematicsArticle