  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
$\operatorname {FDR}$ 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 $\operatorname {FDR}$ procedure. This paper first
introduces a scalar quantity to characterize the extent to which the "lack of
identification phenomenon" ($\operatorname {LIP}$) of the $\operatorname {FDR}$
procedure occurs. Second, we propose a new multiple comparison procedure,
called $\operatorname {FDR}_L$, to accommodate the spatial information of
neighboring $p$-values, via a local aggregation of $p$-values. Theoretical
properties of the $\operatorname {FDR}_L$ procedure are investigated under weak
dependence of $p$-values. It is shown that the $\operatorname {FDR}_L$
procedure alleviates the $\operatorname {LIP}$ of the $\operatorname {FDR}$
procedure, thus substantially facilitating the selection of more stringent
control levels. Simulation evaluations indicate that the $\operatorname
{FDR}_L$ procedure improves the detection sensitivity of the $\operatorname
{FDR}$ procedure with little loss in detection specificity. The computational
simplicity and detection effectiveness of the $\operatorname {FDR}_L$ procedure
are illustrated through a real brain fMRI dataset.
