Shifted BH methods for controlling false discovery rate in multiple testing of the means of correlated normals against two-sided alternatives

For simultaneous testing of multivariate normal means with known correlation matrix against two-sided alternatives, this paper introduces new methods with proven finite-sample control of false discovery rate. The methods are obtained by shifting each $p$-value to the left and considering a Benjamini–Hochberg-type linear step-up procedure based on these shifted $p$-values. The amount of shift for each $p$-value is appropriately determined from the correlation matrix to achieve the desired false discovery rate control. Simulation studies and real-data application show favorable performances of the proposed methods when compared with relevant competitors.