A spatially adaptive large‐scale multiple‐testing procedure

We consider a spatial multiple‐testing problem for large‐scale data with clustered signals. The clustering pattern of signals enlightens us to aggregate the neighbouring information for better statistical inference. We design a novel spatial‐assisted procedure via kernel‐based aggregation, automatically incorporating spatially localized mode of significant signal regions. More specifically, we utilize a sample‐splitting strategy to construct a series of marginal symmetric statistics and a data‐adaptive threshold for false discovery rate (FDR) control. Theoretical results show that the proposed method controls the desired FDR asymptotically under mild conditions. Simulation studies and a functional magnetic resonance imaging data application confirm the advantages of our methodology in terms of FDR control and power improvement.