TABLE 2.

Coverage proportions (Cov) and average lengths (Len) of 95% naïve confidence intervals with tuning parameters ${\lambda }_{sup}$ and ${\lambda }_{\mathit{1}SE}$, and 95% exact post-selection confidence intervals under the stochastic block model setting with partial correlation $\rho \in \{0.2,0.6\}$, sample size $n\in \{100,300,500\}$, dimension $p=100$ and signal-to-noise ratio $\mathrm{S}\mathrm{N}\mathrm{R}\in \{0.1,0.3,0.5\}$. The error variance is estimated either through the scaled lasso (Sun and Zhang, 2012) (SL) or Theorem 2.2 (NL).

$\rho$ $n$ SNR		0.1	100 0.3	0.5	0.1	0.2 300 0.3	0.5	0.1	500 0.3	0.5
	exact ${\lambda }_{\text{sup}}$ SL	0.921	0.934	0.948	0.951	0.934	0.933	0.953	0.958	0.958
Cov	naïve ${\lambda }_{\text{sup}}$ SL	0.540	0.955	0.960	0.953	0.931	0.930	0.966	0.957	0.957
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ SL	0.585	0.850	0.858	0.911	0.922	0.917	0.961	0.944	0.940
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ NL	0.586	0.854	0.865	0.913	0.924	0.918	0.961	0.945	0.942
	exact ${\lambda }_{\text{sup}}$ SL	4.721	1.692	0.857	1.873	0.425	0.325	0.758	0.325	0.252
Len	naïve ${\lambda }_{\text{sup}}$ SL	1.111	0.682	0.545	0.709	0.416	0.323	0.559	0.323	0.251
	naïve ${\lambda }_{\text{1SE}}$ SL	1.188	0.703	0.552	0.715	0.416	0.323	0.557	0.323	0.251
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ NL	1.195	0.710	0.558	0.721	0.420	0.326	0.560	0.325	0.253
$\rho$ $n$ SNR		0.1	100 0.3	0.5	0.1	0.6 300 0.3	0.5	0.1	500 0.3	0.5
	exact ${\lambda }_{\text{sup}}$ SL	0.923	0.945	0.949	0.959	0.956	0.958	0.943	0.948	0.948
Cov	naïve ${\lambda }_{\text{sup}}$ SL	0.569	0.959	0.964	0.964	0.955	0.956	0.963	0.946	0.946
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ SL	0.568	0.841	0.852	0.922	0.933	0.927	0.947	0.946	0.941
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ NL	0.561	0.841	0.850	0.922	0.935	0.929	0.950	0.947	0.943
	exact ${\lambda }_{\text{sup}}$ SL	4.744	1.662	0.832	1.987	0.424	0.325	0.807	0.324	0.251
Len	naïve ${\lambda }_{\text{sup}}$ SL	1.119	0.690	0.545	0.712	0.416	0.323	0.557	0.322	0.250
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ SL	1.194	0.704	0.554	0.713	0.416	0.323	0.555	0.322	0.250
	naïve ${\lambda }_{1\mathrm{S}\mathrm{E}}$ NL	1.194	0.707	0.557	0.718	0.420	0.326	0.558	0.324	0.252