  In multiple testing scenarios, typically the sign of a parameter is inferred
when its estimate exceeds some significance threshold in absolute value.
Typically, the significance threshold is chosen to control the experimentwise
type I error rate, family-wise type I error rate or the false discovery rate.
However, controlling these error rates does not explicitly control the sign
error rate. In this paper, we propose two procedures for adaptively selecting
an experimentwise significance threshold in order to control the sign error
rate. The first controls the sign error rate conservatively, without any
distributional assumptions on the parameters of interest. The second is an
empirical Bayes procedure, and achieves optimal performance asymptotically when
a model for the distribution of the parameters is correctly specified. We also
discuss an adaptive procedure to minimize the sign error rate when the
experimentwise type I error rate is held fixed.
