We believe this work raises some challenges to theoretical statisticians. Our results with genetic simulations would be even more convincing if there were theorems (say for the Wishart case where the data matrix has Gaussian entries) that showed: 1) that using the effective number of markers calculated by Equation 10 instead of the true number of markers does not affect the asymptotics; 2) that the BBP phase change holds for real Wishart matrices as well as for complex; 3) in Figures 2 and 3 the P–P plots show a noticeably better fit at the high end, corresponding to low p-values. Explain!
