The problem of large-scale spatial multiple testing is often encountered in various scientific research fields, where the signals are usually enriched on some regions while sparse on others. To integrate spatial structure information from nearby locations, we propose a novel approach, called {\bf STR}ucture-{\bf A}daptive {\bf W}eighting (STRAW) procedure, for large-scale spatial multiple testing. The STRAW procedure is capable of handling a broad range of spatial settings by leveraging a class of weighted p-values and is fully data-driven. Theoretical results show that the proposed method controls the false discovery rate (FDR) at the pre-specified level under some mild conditions. In practice, the local sparsity level, defined as the probability of the null hypothesis being not true, is commonly unknown. To address this issue, we develop a new method for estimating the local sparsity level by employing the kernel-smooth local false discovery rate (Lfdr) statistic. The superior numerical performance of the STRAW procedure is demonstrated by performing extensive simulation studies and a real data analysis.

翻译：摘要：大规模空间多重检验问题常出现在各类科学研究领域中，其中信号往往在某些区域富集而在其他区域稀疏。为整合邻近位置的空间结构信息，我们提出了一种名为{\bf 结构自适应加权}（STRAW）的新型方法，用于处理大规模空间多重检验。STRAW方法通过利用一类加权p值能够适应广泛的空间设定，且完全由数据驱动。理论结果表明，在温和条件下，该方法能够将错误发现率（FDR）控制在预设水平。实际应用中，局部稀疏水平（定义为原假设不成立的概率）通常是未知的。针对这一问题，我们开发了一种基于核平滑局部错误发现率（Lfdr）统计量估计局部稀疏水平的新方法。通过大量模拟实验和真实数据分析，验证了STRAW方法优越的数值性能。