Table 1.

Simulation results: summary of edge detection under the selected tuning parameter λ by cross-validation for two sets of simulations with p = 50; n = 100 and p = 150; n = 100. The results are the average (standard error) of the number of detected edges, sensitivity, specificity, and mean squared errors(MSE) for θ̂_M over 100 simulation data. Results from glasso and the proposed robust estimation with different specifications of the β value are compared.

Model	Method	# of edges	Sensitivity	Specificity	MSE
p = 50, n = 100
I	glasso	89.22 (1.68)	0.70 (0.0052)	0.97 (0.0012)	0.0032 (0.0000)
	β = 0.02	95.99 (1.83)	0.70 (0.0050)	0.96 (0.0013)	0.0034 (0.0001)
	β = 0.05	94.82 (1.82)	0.69 (0.0053)	0.96 (0.0013)	0.0037 (0.0001)
	β = 0.07	91.10 (1.62)	0.67 (0.0053)	0.96 (0.0011)	0.0039 (0.0001)
II	glasso	306.54 (8.35)	0.76 (0.0065)	0.78 (0.0069)	0.0095 (0.0002)
	β = 0.02	236.82 (11.05)	0.72 (0.0079)	0.84 (0.0092)	0.0083 (0.0002)
	β = 0.05	136.60 (4.67)	0.70 (0.0062)	0.92 (0.0037)	0.0062 (0.0002)
	β = 0.07	110.89 (2.26)	0.68 (0.0058)	0.94 (0.0017)	0.0057 (0.0001)
III	glasso	418.85 (3.22)	0.77 (0.0055)	0.68 (0.0027)	0.014 (0.0003)
	β = 0.02	392.27 (11.99)	0.75 (0.0105)	0.71 (0.0100)	0.014 (0.0003)
	β = 0.05	131.25 (5.35)	0.69 (0.0065)	0.93 (0.0044)	0.0076 (0.0003)
	β = 0.07	105.22 (2.72)	0.67 (0.0057)	0.95 (0.0021)	0.0072 (0.0001)
IV	glasso	441.47 (4.93)	0.77 (0.0079)	0.66 (0.0040)	0.020 (0.0005)
	β = 0.02	430.28 (9.15)	0.75 (0.0107)	0.67 (0.0077)	0.020 (0.0005)
	β = 0.05	133.50 (5.78)	0.70 (0.0071)	0.93 (0.0046)	0.011 (0.0004)
	β = 0.07	109.95 (3.29)	0.68 (0.0069)	0.95 (0.0025)	0.010 (0.0002)
p = 150, n = 100
I	glasso	263.68 (2.38)	0.64 (0.0027)	0.99 (0.0002)	0.0015 (0.0001)
	β = 0.005	281.33 (2.73)	0.64 (0.0027)	0.99 (0.0002)	0.0015 (0.0001)
	β = 0.02	281.94 (2.61)	0.64 (0.0027)	0.99 (0.0002)	0.0016 (0.0001)
	β = 0.03	276.03 (2.82)	0.63 (0.0030)	0.99 (0.0002)	0.0017 (0.0001)
II	glasso	682.78 (1.63)	0.60 (0.0063)	0.95 (0.0002)	0.0030 (0.0001)
	β = 0.005	637.32 (9.14)	0.64 (0.0052)	0.95 (0.0008)	0.0031 (0.0001)
	β = 0.02	427.60 (7.39)	0.65 (0.0034)	0.97 (0.0006)	0.0027 (0.0001)
	β = 0.03	335.24 (4.46)	0.63(0.0033)	0.98 (0.0004)	0.0025 (0.0001)
III	glasso	507.70 (24.71)	0.40 (0.0091)	0.96 (0.0021)	0.0039 (0.0001)
	β = 0.005	672.33 (6.22)	0.54 (0.0087)	0.95 (0.0006)	0.0040 (0.0001)
	β = 0.02	469.63 (10.29)	0.66 (0.0043)	0.97 (0.0009)	0.0037 (0.0001)
	β = 0.03	363.00 (7.63)	0.63 (0.0038)	0.98 (0.0006)	0.0034 (0.0001)
IV	glasso	678.70 (4.00)	0.38 (0.0033)	0.95 (0.0004)	0.0046 (0.0001)
	β = 0.005	673.54 (2.46)	0.52 (0.0081)	0.95 (0.0003)	0.0049 (0.0001)
	β = 0.02	487.78 (12.59)	0.66 (0.0041)	0.97 (0.0011)	0.0038 (0.0001)
	β = 0.03	370.41 (9.31)	0.63 (0.0042)	0.98(0.0008)	0.0033 (0.0001)