Table 4 Simulation Results for the Independent Models
| Â | Â | Â | FDR | Power | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
n | m 1 | δ | P-val | P-adm | Convex | Pareto | P-val | P-adm | Convex | Pareto |
10 | 50 | 1.0 | 5.4 | 3.7 | 3.4 | 3.4 | 2.1 | 2.8 | 2.8 | 2.9 |
| Â | Â | 1.2 | 5.4 | 3.3 | 3.0 | 2.8 | 7.0 | 8.3 | 8.3 | 8.7 |
| Â | Â | 1.4 | 5.1 | 3.0 | 2.9 | 2.7 | 20.8 | 22.5 | 23.0 | 24.0 |
| Â | Â | 1.6 | 5.0 | 3.0 | 3.0 | 2.9 | 40.4 | 42.2 | 43.2 | 44.3 |
| Â | Â | 1.8 | 4.7 | 2.8 | 2.8 | 2.8 | 62.1 | 64.2 | 65.2 | 65.8 |
| Â | Â | 2.0 | 4.9 | 2.9 | 3.1 | 3.1 | 77.9 | 80.3 | 81.2 | 81.9 |
| Â | Â | 2.5 | 5.1 | 4.6 | 4.6 | 5.1 | 96.4 | 97.9 | 98.0 | 98.2 |
| Â | Â | 3.0 | 5.0 | 5.1 | 5.1 | 5.2 | 99.7 | 100.0 | 100.0 | 100.0 |
| Â | 100 | 1.0 | 5.0 | 2.9 | 2.8 | 2.5 | 3.3 | 3.9 | 4.0 | 4.2 |
| Â | Â | 1.2 | 5.2 | 3.0 | 3.3 | 3.1 | 13.9 | 14.9 | 15.2 | 15.8 |
| Â | Â | 1.4 | 4.7 | 2.7 | 2.9 | 2.8 | 34.4 | 35.7 | 36.2 | 36.9 |
| Â | Â | 1.6 | 4.5 | 2.7 | 2.9 | 2.8 | 56.1 | 57.7 | 58.4 | 59.1 |
| Â | Â | 1.8 | 4.5 | 2.8 | 3.0 | 2.8 | 74.5 | 76.3 | 76.9 | 77.5 |
| Â | Â | 2.0 | 4.7 | 3.0 | 3.3 | 2.8 | 87.0 | 88.9 | 89.2 | 89.6 |
| Â | Â | 2.5 | 4.8 | 4.3 | 4.5 | 4.9 | 98.3 | 99.2 | 99.3 | 99.3 |
| Â | Â | 3.0 | 4.6 | 5.1 | 5.1 | 5.2 | 99.9 | 100.0 | 100.0 | 100.0 |
15 | 50 | 1.0 | 4.2 | 3.1 | 3.3 | 3.1 | 13.6 | 15.0 | 15.1 | 15.7 |
| Â | Â | 1.2 | 4.6 | 3.1 | 3.2 | 3.3 | 37.4 | 38.9 | 39.7 | 40.6 |
| Â | Â | 1.4 | 4.8 | 3.3 | 3.5 | 3.5 | 63.5 | 65.5 | 66.2 | 66.8 |
| Â | Â | 1.6 | 4.9 | 3.6 | 3.8 | 4.0 | 82.8 | 84.6 | 85.2 | 85.7 |
| Â | Â | 1.8 | 4.9 | 4.2 | 4.3 | 4.9 | 93.3 | 94.7 | 95.1 | 95.2 |
| Â | Â | 2.0 | 4.7 | 4.8 | 4.9 | 5.1 | 97.7 | 98.6 | 98.7 | 98.7 |
| Â | Â | 2.5 | 4.5 | 5.0 | 4.9 | 5.1 | 99.9 | 100.0 | 100.0 | 100.0 |
| Â | Â | 3.0 | 4.7 | 5.1 | 5.0 | 5.2 | 100.0 | 100.0 | 100.0 | 100.0 |
15 | 100 | 1.0 | 4.7 | 3.1 | 3.2 | 3.1 | 22.3 | 23.2 | 23.6 | 24.2 |
| Â | Â | 1.2 | 4.6 | 3.1 | 3.3 | 3.3 | 50.0 | 51.2 | 51.8 | 52.4 |
| Â | Â | 1.4 | 4.6 | 3.3 | 3.5 | 3.6 | 74.2 | 75.7 | 76.2 | 76.7 |
| Â | Â | 1.6 | 4.5 | 3.4 | 3.7 | 3.8 | 89.0 | 90.3 | 90.7 | 90.9 |
| Â | Â | 1.8 | 4.5 | 3.9 | 4.1 | 4.3 | 96.0 | 97.1 | 97.2 | 97.3 |
| Â | Â | 2.0 | 4.5 | 4.5 | 4.6 | 4.9 | 98.8 | 99.3 | 99.4 | 99.4 |
| Â | Â | 2.5 | 4.6 | 5.0 | 5.1 | 5.2 | 100.0 | 100.0 | 100.0 | 100.0 |
| Â | Â | 3.0 | 4.5 | 5.1 | 5.0 | 5.2 | 100.0 | 100.0 | 100.0 | 100.0 |