Table 2:

Simulation II results: the means of PEs and MSEs for regularized low-rank (RLR) OLS, Lasso, fused Lasso (Fused) and tensor envelope (Envelope) estimates and their associated standard errors in the parentheses. For each case, 100 simulated data sets are used.

(n, ${\sigma }_e^2$	Method	MSE(B1)	MSE(B2)	PE
(100, 1)	RLR	21.86(0.33)	13.91(0.20)	1.02(0.0001)
	OLS	41.85(0.16)	56.82(0.82)	1.03(0.0003)
	Lasso	55.78(0.88)	54.40(0.73)	1.03(0.0002)
	Fused	57.39(0.94)	56.61(0.77)	1.03(0.0002)
	Envelope	41.46(0.15)	33.23(0.54)	1.02(0.0002)
(200, 1)	RLR	10.84(0.12)	6.77(0.07)	1.011(0.00005)
	OLS	20.75(0.07)	27.80(0.30)	1.018(0.0001)
	Lasso	27.90(0.31)	27.03(0.29)	1.018(0.0001)
	Fused	27.69(0.30)	27.29(0.29)	1.018(0.0001)
	Envelope	20.68(0.07)	18.33(0.22)	1.014(0.00008)
(500, 1)	RLR	4.19(0.05)	2.73(0.02)	1.004(0.00002)
	OLS	8.22(0.03)	10.94(0.08)	1.006(0.00003)
	Lasso	12.49(0.18)	12.18(0.17)	1.007(0.00006)
	Fused	10.99(0.08)	10.91(0.09)	1.006(0.00003)
	Envelope	8.26(0.03)	9.37(0.09)	1.006(0.00003)
(100, 25)	RLR	391.95(5.50)	254.67(3.54)	25.37(0.0024)
	OLS	1044(4.10)	1447(23.94)	25.77(0.0060)
	Lasso	1378.32(22.99)	1360.95(18.52)	25.75(0.0059)
	Fused	1232.31(17.74)	1042.72(12.13)	25.68(0.0055)
	Envelope	1033.69(3.66)	626.57(7.71)	25.46(0.0027)
(200, 25)	RLR	219.13(2.14)	136.41(1.33)	25.26(0.0011)
	OLS	518.63(1.83)	694.98(7.47)	25.45(0.0025)
	Lasso	657.39(7.19)	644.78(7.20)	25.44(0.0025)
	Fused	637.01(6.45)	589.9(5.68)	25.43(0.0022)
	Envelope	516.52(1.81)	395.64(3.67)	25.33(0.0015)
(500, 25)	RLR	101.8(0.91)	64.19(0.57)	25.09(0.0005)
	OLS	206.57(0.73)	275.3(2.05)	25.16(0.0008)
	Lasso	259.2(1.95)	254.26(2.17)	25.16(0.0008)
	Fused	265.44(1.89)	255.88(1.99)	25.16(0.0008)
	Envelope	206.41(0.73)	226.94(1.54)	25.14(0.0006)