Figure 4.

Comparing type I error rates (a),(b) and power (c),(d) of the competing tests at 0.05 p-value cutoff, with complex correlation patterns. For (a) and (c), p = 20, n = 50. For (b) and (d), p = 20, n = 10. For the three types of correlations, ${\sigma }_{ii}^{\prime }\propto i(i=1,\cdots ,p)$. For ${\mathbf{\Sigma }}_1^{\prime },{\sigma }_{ij}^{\prime }=0$. For ${\mathbf{\Sigma }}_2^{\prime },{\rho }_{ij}^{\prime }~0\cup N(0.5,{0.1}^2)$, and ${\sigma }_{ij}^{\prime }={\rho }_{ij}^{\prime }\sqrt{{\sigma }_{ii}^{\prime }{\sigma }_{jj}^{\prime }}$. For ${\mathbf{\Sigma }}_3^{\prime },{\sigma }_{ij}^{\prime }={0.8}^{|i-j|}\sqrt{{\sigma }_{ii}^{\prime }{\sigma }_{jj}^{\prime }}$.