Table 1.
Mean L1 losses (and standard deviations) for the different methods
| Type | CLASSO | SPICE | ACLASSO | CSCAD | BCLASSOm | BCLASSOs | |
|---|---|---|---|---|---|---|---|
| Sparse | Θ | 2.38(0.43) | 4.18(1.91) | 5.71(2.62) | 14.27(12.18) | 4.82 (1.11) | 4.52 (0.87) |
| Σ | 4.03(1.03) | 2.99(0.76) | 5.65(1.42) | 19.02(7.92) | 13.65(1.70) | 3.56 (0.67) | |
| Moderately | Θ | 3.29(0.52) | 5.09(2.69) | 6.07(2.74) | 13.44(8.80) | 6.09 (1.29) | 5.79 (1.03) |
| Sparse | Σ | 5.76(1.42) | 4.17(0.77) | 6.41(1.25) | 22.84(9.61) | 12.93(1.89) | 5.10 (0.87) |
| Dense | Θ | 4.90(0.53) | 7.08(1.83) | 7.65(2.46) | 17.22(11.49) | 6.87 (1.17) | 6.39 (0.87) |
| Σ | 9.53(2.24) | 6.35(1.04) | 9.95(1.31) | 31.91(27.49) | 12.82(1.80) | 6.04 (0.69) | |
| AR(1) | Θ | 5.44(0.57) | 7.60(2.16) | 8.12(2.14) | 13.11(7.14) | 7.02 (1.15) | 7.00 (0.87) |
| Σ | 9.53(2.24) | 7.48(1.29) | 7.95(1.31) | 31.91(27.49) | 12.42(5.97) | 5.97 (0.59) | |
| Tridiagonal | Θ | 5.70(0.57) | 7.99(1.83) | 7.80(2.32) | 19.45(9.45) | 10.43(1.42) | 9.27 (0.95) |
| Σ | 11.37(2.65) | 9.37(1.79) | 9.19(1.48) | 24.50(9.10) | 12.79(1.82) | 12.18(1.16) | |
| Diagonal | Θ | 2.41(2.75) | 3.69(2.11) | 7.00(3.79) | 10.49(5.87) | 4.31 (1.46) | 3.98 (0.98) |
| Σ | 4.23(4.74) | 2.43(0.79) | 7.27(5.44) | 18.47(9.72) | 13.81(1.67) | 4.47 (0.99) |
Note: CLASSO = covariance lasso; ACLASSO = adaptive covariance lasso; SPICE = sparse permutation invariant covariance estimator; ACLASSO = adaptive covariance lasso; CSCAD = smoothly clipped absolute deviation for covariance; BCLASSOm = Bayesian covariance; lasso with L1 minimax estimator; BCLASSOs = Bayesian covariance lasso with sparsity forced;