Abstract

Exploiting spatial patterns in large-scale multiple testing promises to improve both power and interpretability of false discovery rate (FDR) analyses. This article develops a new class of locally adaptive weighting and screening (LAWS) rules that directly incorporates useful local patterns into inference. The idea involves constructing robust and structure-adaptive weights according to the estimated local sparsity levels. LAWS provides a unified framework for a broad range of spatial problems and is fully data-driven. It is shown that LAWS controls the FDR asymptotically under mild conditions on dependence. The finite sample performance is investigated using simulated data, which demonstrates that LAWS controls the FDR and outperforms existing methods in power. The efficiency gain is substantial in many settings. We further illustrate the merits of LAWS through applications to the analysis of two-dimensional and three-dimensional images. Supplementary materials for this article are available online.

摘要

在大规模多重测试中利用空间模式有望提高错误发现率 (FDR) 分析的能力和可解释性。本文开发了一类新的局部自适应加权和筛选 (L​​AWS) 规则，该规则直接将有用的局部模式纳入推理。该想法涉及根据估计的局部稀疏程度构建稳健和结构自适应的权重。LAWS 为广泛的空间问题提供了一个统一的框架，并且完全由数据驱动。结果表明，LAWS 在依赖的温和条件下渐近地控制 FDR。使用模拟数据研究了有限样本的性能，这表明 LAWS 控制了 FDR 并在功率方面优于现有方法。在许多环境中，效率增益是可观的。我们通过对二维和三维图像分析的应用进一步说明了 LAWS 的优点。本文的补充材料可在线获取。