Table 3.
Median MSEs based on 100 simulation replications in Example 3. Here Full, True, Lasso, OSCAR, E-NET, Convex, DCE denote the least squares estimates based on the full model, the true model, the Lasso estimate, the elastic net estimate, the OSCAR estimate, our convex counterpart based on iteration m = 0, and our estimate. Note that the results for OSCAR and E-NET in Examples 4 and 5 of Bondell and Reich (2008) with σ = 15 are taken from Table 1 there.
| Bondell & Reich | σ | Full | True model | Lasso | E-NET | OSCAR | Our | Ave # Iter | Ave match proportion | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Group | Variable | Conv | DCE | ||||||||
| Ex 4 | 15 | 95.1 | 6.2 | 47.4 | 45.4 | 34.4 | 25.9 | 21.4 | 22.0 | 2 | 0.516 |
| Ex 5 | 15 | 174.8 | 11.6 | 67.4 | 64.7 | 40.7 | 51.8 | 67.6 | 70.0 | 4 | 0.535 |
| 10 | 77.7 | 5.1 | 30.0 | 33.1 | 35.3 | 38.0 | 4 | 0.575 | |||
| 5 | 19.4 | 1.3 | 7.5 | 10.7 | 10.4 | 6.0 | 4.5 | 0.626 | |||
| 1 | 0.86 | 0.05 | 0.30 | 0.47 | 0.43 | 0.06 | 3 | 0.703 | |||