It is frequently of interest to jointly analyze multiple sequences of
multiple tests in order to identify simultaneous signals, defined as features
tested in multiple studies whose test statistics are non-null in each. In many
problems, however, the null distributions of the test statistics may be
complicated or even unknown, and there do not currently exist any procedures
that can be employed in these cases. This paper proposes a new nonparametric
procedure that can identify simultaneous signals across multiple studies even
without knowing the null distributions of the test statistics. The method is
shown to asymptotically control the false discovery rate, and in simulations
had excellent power and error control. In an analysis of gene expression and
histone acetylation patterns in the brains of mice exposed to a conspecific
intruder, it identified genes that were both differentially expressed and next
to differentially accessible chromatin. The proposed method is available in the
R package github.com/sdzhao/ssa
