05874507

j

05874507 Zhang, Chunming Fan, Jianqing Yu, Tao Multiple testing via $\mathrm{FDR}_L$ for large-scale imaging data. Ann. Stat. 39, No. 1, 613-642 (2011). 2011 Institute of Mathematical Statistics, Beachwood, OH EN brain fMRI false discovery rate median filtering $p$-value sensitivity specificity

doi:10.1214/10-AOS848

Summary: The multiple testing procedure plays an important role in detecting the presence of spatial signals for large-scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional false discovery rate (FDR) procedure can lack the ability to detect statistical significance, even if the $p$-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the ``lack of identification phenomenon'' (LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR$_L$, to accommodate the spatial information of neighboring $p$-values, via a local aggregation of $p$-values. Theoretical properties of the FDR$_L$ procedure are investigated under weak dependence of $p$-values. It is shown that the FDR$_L$ procedure alleviates the LIP of the FDR procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the FDR$_L$ procedure improves the detection sensitivity of the FDR procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the FDR$_L$ procedure are illustrated through a real brain fMRI dataset.