Research Article
Group Identification and Variable Selection in Quantile Regression
Table 3
ME, SA, GA, and SGA results of Example
3 for n=100.
| ā | | Criterion | Ridge | QR- | QR- | QR- | QR- | QR-PACS | QR | LASSO | SCAD | adaptive LASSO | elastic-net |
| =1 | 0.10 | ME(S.E) | 0.1383(0.0195) | 0.1176(0.0196) | 0.0933(0.0164) | 0.0908(0.0151) | 0.0902(0.0119) | 0.0558(0.0098) | SA | 0 | 58 | 79 | 79 | 82 | 78 | GA | 0 | 0 | 0 | 0 | 0 | 85 | SGA | 0 | 0 | 0 | 0 | 0 | 70 | 0.50 | ME(S.E) | 0.1139(0.0071) | 0.0843(0.0062) | 0.0662(0.0059) | 0.0643(0.0054) | 0.0638(0.0051) | 0.0367(0.0029) | SA | 0 | 62 | 80 | 81 | 84 | 79 | GA | 0 | 0 | 0 | 0 | 0 | 86 | SGA | 0 | 0 | 0 | 0 | 0 | 71 | 0.75 | ME(S.E) | 0.1289(0.0180) | 0.1083(0.0171) | 0.0861(0.0161) | 0.0843(0.0147) | 0.0834(0.0108) | 0.0479(0.0081) | SA | 0 | 61 | 80 | 80 | 84 | 79 | GA | 0 | 0 | 0 | 0 | 0 | 86 | SGA | 0 | 0 | 0 | 0 | 0 | 71 |
| =3 | 0.10 | ME(S.E) | 0.1490(0.0199) | 0.1279(0.0198) | 0.1030(0.0169) | 0.1016(0.0155) | 0.0998(0.0124) | 0.0651(0.0104) | SA | 0 | 57 | 78 | 78 | 80 | 77 | GA | 0 | 0 | 0 | 0 | 0 | 83 | SGA | 0 | 0 | 0 | 0 | 0 | 69 | 0.50 | ME(S.E) | 0.1244(0.0076) | 0.0945(0.0065) | 0.0867(0.0062) | 0.0742(0.0056) | 0.0735(0.0054) | 0.0464(0.0032) | SA | 0 | 61 | 79 | 80 | 83 | 78 | GA | 0 | 0 | 0 | 0 | 0 | 85 | SGA | 0 | 0 | 0 | 0 | 0 | 70 | 0.75 | ME(S.E) | 0.1399(0.0185) | 0.1189(0.0171) | 0.0958(0.0166) | 0.0946(0.0160) | 0.0930(0.0111) | 0.0567(0.0086) | SA | 0 | 60 | 79 | 80 | 83 | 78 | GA | 0 | 0 | 0 | 0 | 0 | 85 | SGA | 0 | 0 | 0 | 0 | 0 | 70 |
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