Global testing against sparse alternatives in time-frequency analysis
提出过采样周期图高阶批评检验，用于全局检测复值时间序列中的稀疏周期效应，并建立了可检测边界，证明该检验在可检测区域渐近有效。
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.