Abstract: Clustered effects are often encountered in multiple hypothesis testing of spatial signals. In this paper, we propose a new method, termed two-dimensional spatial multiple testing (2D-SMT) procedure, to control the false discovery rate (FDR) and improve the detection power by exploiting the spatial information encoded in neighboring observations. The proposed method provides a novel perspective of utilizing spatial information by gathering signal patterns and spatial dependence into an auxiliary statistic. 2D-SMT rejects the null when a primary statistic at the location of interest and the auxiliary statistic constructed based on nearby observations are greater than their corresponding cutoffs. 2D-SMT can also be combined with different variants of the weighted BH procedures to improve the detection power further. A fast algorithm is developed to accelerate the search for optimal cutoffs in 2D-SMT. In theory, we establish the asymptotic FDR control of 2D-SMT under weak spatial dependence. Extensive numerical experiments demonstrate that the 2D-SMT method combined with various weighted BH procedures achieves the most competitive performance in FDR and power trade-off.

Key words and phrases: Empirical Bayes, false discovery rate, near epoch dependence, side information.