. Author manuscript; available in PMC: 2017 Sep 1.

Published in final edited form as: J Multivar Anal. 2016 May 19;150:55–74. doi: 10.1016/j.jmva.2016.05.002

Table 2.

Comparsion between ${\hat{Σ}}^{at}$ and ${\hat{Σ}}^{at •}$ in different settings of sparse covariance matrix estimation.

	Spectral norm		ℓ₁ norm		Frobenius norm
(p, n)	${\hat{Σ}}^{at}$	${\hat{Σ}}^{at •}$	${\hat{Σ}}^{at}$	${\hat{Σ}}^{at •}$	${\hat{Σ}}^{at}$	${\hat{Σ}}^{at •}$
Permutation Bandable Model, MUCR ρ = .5
(50, 50)	4.26(0.24)	4.45(0.41)	5.58(0.58)	6.19(7.54)	11.34(0.79)	11.73(1.08)
(50, 200)	1.70(0.05)	1.74(0.06)	3.31(0.32)	3.42(0.38)	4.93(0.09)	5.07(0.16)
(200, 100)	3.48(0.07)	3.66(0.58)	5.80(0.39)	6.23(14.89)	18.34(0.81)	19.37(5.50)
(200, 200)	2.12(0.04)	2.20(0.03)	4.17(0.29)	4.44(0.32)	11.46(0.14)	11.94(0.13)
(500, 200)	2.28(0.03)	3.51(0.17)	4.17(0.15)	6.55(0.72)	16.85(0.10)	21.96(0.49)
Randomly Sparse Model, MUCR ρ = .5
(50, 50)	1.76(0.07)	1.96(0.62)	3.69(0.24)	4.20(5.89)	5.75(0.51)	6.27(2.95)
(50, 200)	1.05(0.00)	1.06(0.00)	2.73(0.04)	2.74(0.05)	3.75(0.03)	3.77(0.04)
(200, 100)	1.40(0.01)	1.45(0.01)	4.88(0.08)	4.94(0.09)	8.34(0.07)	8.50(0.07)
(200, 200)	1.07(0.00)	1.09(0.01)	4.44(0.03)	4.46(0.03)	7.42(0.02)	7.43(0.02)
(500, 200)	1.14(0.01)	1.31(0.01)	6.39(0.04)	6.65(0.08)	11.73(0.01)	12.23(0.05)
Permutation Bandable Model, MCR ρ⁽¹⁾ = .8, ρ⁽²⁾ = .2
(50, 50)	4.23(0.38)	4.71(1.17)	6.67(2.30)	7.46(8.92)	11.22(1.34)	11.71(2.01)
(50, 200)	1.64(0.05)	2.79(0.39)	2.94(0.21)	4.52(0.95)	4.41(0.13)	6.29(0.46)
(200, 100)	3.17(0.06)	4.16(0.57)	5.73(0.66)	8.11(1.87)	15.93(0.53)	18.03(0.77)
(200, 200)	2.00(0.03)	3.22(0.18)	3.65(0.16)	5.70(0.60)	9.83(0.11)	13.29(0.55)
(500, 200)	2.22(0.03)	3.45(0.17)	4.09(0.17)	6.44(0.96)	16.80(0.14)	21.93(0.45)
Randomly Sparse Model, MCR ρ⁽¹⁾ = .8, ρ⁽²⁾ = .2
(50, 50)	2.15(0.46)	2.19(0.49)	4.21(0.94)	4.47(4.65)	6.36(0.96)	7.25(1.57)
(50, 200)	1.09(0.02)	1.16(0.04)	2.82(0.19)	2.99(0.32)	3.83(0.10)	4.00(0.20)
(200, 100)	1.46(0.02)	1.82(0.03)	4.96(0.12)	5.61(0.21)	8.45(0.07)	10.10(0.14)
(200, 200)	1.08(0.00)	1.20(0.01)	4.46(0.04)	4.57(0.05)	7.43(0.02)	7.66(0.04)
(500, 200)	1.12(0.01)	1.33(0.01)	6.35(0.04)	6.60(0.07)	11.71(0.02)	12.20(0.06)