This paper studies the classical problem of estimating the locations of signal occurrences in a noisy measurement. Based on a multiple hypothesis testing scheme, we design a K-sample statistical test to control the false discovery rate (FDR). Specifically, we first convolve the noisy measurement with a smoothing kernel, and find all local maxima. Then, we evaluate the joint probability of K entries in the vicinity of each local maximum, derive the corresponding p-value, and apply the Benjamini-Hochberg procedure to account for multiplicity. We demonstrate through extensive experiments that our proposed method, with K=2, controls the prescribed FDR while increasing the power compared to a one-sample test.

中文翻译：

---

用于信号检测的 K 样本多重假设检验

本文研究了在噪声测量中估计信号出现位置的经典问题。基于多假设检验方案，我们设计了一个 K 样本统计检验来控制错误发现率 (FDR)。具体来说，我们首先将噪声测量与平滑核进行卷积，并找到所有局部最大值。然后，我们评估每个局部最大值附近的 K 个条目的联合概率，得出相应的 p 值，并应用 Benjamini-Hochberg 程序来解释多重性。我们通过大量实验证明，与单样本测试相比，我们提出的方法（K=2）控制了规定的 FDR，同时增加了功率。