Optimal Statistic for multiple cross correlated signals

The optimal statistic is a frequentist method to estimate the amplitude of the stochastic GWB. In presvious analyses, we have calculated the optimal statistic for single, cross-correlated signals. To test the ability of the optimal statistic to retrieve multiple cross-correlated signals with different ORFs, we have created simulated timing residuals that contain a Hellings-Downs signal, or a GW-like monopole signal. We compare the recovered amplitudes and confidence intervals for these simulated data sets using different numbers of cross-correlated signals