STRAW: Structure-Adaptive Weighting Procedure for Large-Scale Spatial Multiple Testing

TL;DR

The paper introduces STRAW, a data-driven, structure-adaptive weighting method for large-scale spatial multiple testing that effectively controls FDR and adapts to varying local sparsity levels, demonstrated through simulations and real data.

Contribution

The paper proposes a novel, fully data-driven spatial multiple testing procedure that leverages weighted p-values and estimates local sparsity, controlling FDR in diverse spatial settings.

Findings

Controls FDR at the desired level under mild conditions.

Outperforms existing methods in simulations and real data.

Effectively estimates local sparsity using kernel-smoothed Lfdr.

Abstract

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.