Table A8.
Summary results under simulation scenarios with some weak signals. In each cell, mean (sd) based on 200 replicates.
| M:TP | M:FP | I:TP | I:FP | RSSE | PMSE | |
|---|---|---|---|---|---|---|
| D1: N(0,1) | ||||||
| LTS-MCP-Hier | 8.0(0.2) | 0.4(1.2) | 8.0(1.4) | 0.6(0.7) | 1.54(0.32) | 0.92(0.25) |
| LS-MCP | 6.7(0.9) | 2.3(3.0) | 7.7(1.3) | 9.5(10.2) | 2.14(0.45) | 1.07(0.39) |
| LAD-Lasso | 8.0(0.0) | 5.7(3.2) | 8.6(1.3) | 16.5(8.3) | 1.44(0.26) | 1.21(0.32) |
| RLARS | 7.8(0.4) | 0.2(0.6) | 5.0(1.5) | 8.2(5.6) | 2.43(0.41) | 1.45(0.41) |
| LTS-MCP | 6.8(0.8) | 6.9(3.7) | 7.2(1.4) | 25.3(9.1) | 2.03(0.46) | 0.97(0.22) |
| LS-MCP-Hier | 8.0(0.0) | 0.5(1.0) | 9.0(1.2) | 0.7(0.7) | 1.38(0.21) | 0.76(0.14) |
| D2: 0.9N(0,1) + 0.1Cauchy(0,5) | ||||||
| LTS-MCP-Hier | 8.0(0.1) | 0.6(1.4) | 8.3(1.4) | 0.8(0.9) | 1.56(0.26) | 0.89(0.20) |
| LS-MCP | 1.8(1.7) | 18.9(8.0) | 1.5(1.5) | 73.9(10.1) | 38.28(56.15) | 761.65(2767.61) |
| LAD-Lasso | 8.0(0.2) | 2.3(1.5) | 5.8(1.6) | 7.3(2.4) | 2.03(0.30) | 1.96(0.58) |
| RLARS | 7.6(0.6) | 0.8(1.1) | 4.3(1.4) | 10.3(6.8) | 2.71(0.39) | 1.82(0.58) |
| LTS-MCP | 6.7(0.9) | 8.2(3.8) | 7.1(1.4) | 31.1(10.3) | 2.12(0.49) | 1.00(0.27) |
| LS-MCP-Hier | 5.5(1.5) | 166.6(124.1) | 1.3(1.6) | 31.3(79.7) | 32.79(45.78) | 1446.11(5735.58) |
| D3: 0.9N(0,1) + 0.1N(20,1) | ||||||
| LTS-MCP-Hier | 8.0(0.1) | 0.4(1.2) | 8.6(1.4) | 0.7(0.9) | 1.48(0.24) | 0.82(0.18) |
| LS-MCP | 2.9(1.1) | 25.2(5.4) | 2.0(1.0) | 67.4(5.0) | 9.44(0.63) | 31.63(6.25) |
| LAD-Lasso | 7.9(0.3) | 2.6(1.7) | 5.1(1.7) | 7.8(2.4) | 2.18(0.36) | 2.29(0.77) |
| RLARS | 6.5(1.1) | 1.4(1.4) | 3.0(1.4) | 11.6(5.7) | 3.31(0.40) | 3.04(1.08) |
| LTS-MCP | 6.8(0.9) | 6.5(3.2) | 7.4(1.2) | 28.2(9.1) | 2.01(0.48) | 0.93(0.20) |
| LS-MCP-Hier | 5.9(1.0) | 93.1(6.0) | 1.7(1.4) | 5.4(4.6) | 8.07(0.52) | 28.15(5.19) |
| D4: N(0,1) and with leverage points | ||||||
| LTS-MCP-Hier | 7.8(0.6) | 1.4(2.7) | 7.7(2.0) | 1.4(1.8) | 1.75(0.54) | 1.01(0.93) |
| LS-MCP | 1.5(0.9) | 22.1(4.8) | 2.3(1.4) | 69.4(6.4) | 6.41(0.85) | 14.50(4.92) |
| LAD-Lasso | 4.5(1.2) | 4.0(2.2) | 3.2(1.8) | 14.2(3.5) | 3.27(0.32) | 6.70(1.77) |
| RLARS | 7.6(0.6) | 0.5(0.7) | 5.0(1.4) | 10.1(6.3) | 2.53(0.38) | 1.65(0.59) |
| LTS-MCP | 6.5(1.2) | 6.7(4.3) | 7.2(1.4) | 27.0(12.7) | 2.12(0.58) | 1.30(0.35) |
| LS-MCP-Hier | 5.5(1.3) | 27.1(29.1) | 3.7(2.4) | 5.1(2.7) | 3.99(0.85) | 7.47(4.51) |
| D5: 0.9N(0,1) + 0.1Cauchy(0,5) and with leverage points | ||||||
| LTS-MCP-Hier | 7.7(0.9) | 1.5(2.8) | 8.0(2.1) | 1.3(1.3) | 1.76(0.53) | 1.04(1.04) |
| LS-MCP | 0.5(0.8) | 17.1(8.9) | 1.1(1.1) | 69.2(18.5) | 32.48(44.17) | 600.83(2389.98) |
| LAD-Lasso | 4.5(1.4) | 4.0(2.1) | 3.5(1.8) | 12.6(3.4) | 3.28(0.32) | 6.54(1.70) |
| RLARS | 7.3(0.7) | 1.0(1.1) | 4.3(1.7) | 11.3(6.7) | 2.81(0.39) | 1.98(0.63) |
| LTS-MCP | 6.7(0.9) | 8.4(3.9) | 7.0(1.4) | 32.0(10.5) | 2.17(0.51) | 1.31(0.29) |
| LS-MCP-Hier | 4.4(1.5) | 168.7(117.3) | 1.0(1.5) | 27.6(71.1) | 31.14(43.24) | 1186.95(4305.08) |