Global testing against sparse alternatives in time-frequency analysis
T. Tony Cai, Yonina C. Eldar, Xiaodong Li
The Annals of Statistics · 2016 · Volume 44 · Issue 4
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.
Keywords
62C20, 62F03, 62F05, 62G30, 62G32, Detection boundary, Empirical processes, higher criticism, over-sampled periodogram, Sparsity, Testing for periodicity
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