Table 1.
MSEs as well as estimated standard errors (in parentheses) of grouping pursuit for various methods based on 100 simulation replications in Example 1. Here Full, True, Lasso, Convex, DCE, denote the least squares estimates based on the full model, the true model, the Lasso estimate, our convex counterpart based on iteration m = 0, and our estimate.
| n | σ | Full | True model | Lasso | Our | Ave # Iter | Ave match proportion | ||
|---|---|---|---|---|---|---|---|---|---|
| Grouping | Variable | Convex | DCE | ||||||
| 50 | 2.0 | 1.607 (0.0446) |
0.235 (0.0150) |
0.845 (0.0310) |
1.318 (0.0449) |
1.418 (0.0483) |
0.837 (0.0721) |
4.31 (0.17) |
0.633 |
| 1.0 | 0.402 (0.0111) |
0.059 (0.0037) |
0.211 (0.0077) |
0.330 (0.0112) |
0.362 (0.0128) |
0.070 (0.0050) |
4.08 (0.14) |
0.716 | |
| 0.5 | 0.100 (0.0028) |
0.015 (0.0009) |
0.053 (0.0019) |
0.083 (0.0029) |
0.091 (0.0032) |
0.019 (0.0016) |
3.71 (0.10) |
0.733 | |
| 100 | 2.0 | 0.833 (0.0244) |
0.129 (0.0083) |
0.456 (0.0176) |
0.658 (0.0229) |
0.699 (0.0234) |
0.183 (0.0157) |
4.32 (0.16) |
0.788 |
| 1.0 | 0.208 (0.0061) |
0.032 (0.0021) |
0.114 (0.0044) |
0.164 (0.0058) |
0.175 (0.0059) |
0.040 (0.0035) |
3.94 (0.12) |
0.867 | |
| 0.5 | 0.052 (0.0015) |
0.008 (0.0005) |
0.028 (0.0011) |
0.041 (0.0014) |
0.044 (0.0015) |
0.010 (0.0008) |
3.16 (0.06) |
0.887 | |
| 200 | 2.0 | 0.411 (0.0123) |
0.060 (0.0041) |
0.223 (0.0092) |
0.335 (0.0117) |
0.364 (0.0129) |
0.080 (0.0057) |
4.03 (0.13) |
0.926 |
| 1.0 | 0.103 (0.0031) |
0.015 (0.0010) |
0.056 (0.0023) |
0.084 (0.0029) |
0.091 (0.0032) |
0.020 (0.0014) |
3.33 (0.06) |
0.950 | |
| 0.5 | 0.026 (0.0008) |
0.004 (0.0003) |
0.014 (0.0006) |
0.022 (0.0008) |
0.023 (0.0008) |
0.005 (0.0003) |
2.98 (0.01) |
0.960 | |