Date of this Version
The Annals of Statistics
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
The original and published work is available at: https://projecteuclid.org/euclid.aos/1467894704
Testing for periodicity, sparsity, over-sampled periodogram, higher criticism, detection boundary, empirical processes
Cai, T., Eldar, Y. C., & Li, X. (2016). Global Testing Against Sparse Alternatives in Time-Frequency Analysis. The Annals of Statistics, 44 (4), 1438-1466. http://dx.doi.org/10.1214/15-AOS1412
Date Posted: 27 November 2017
This document has been peer reviewed.