Group Identification and Variable Selection in Quantile Regression

Table 3

ME, SA, GA, and SGA results of Example 3 for n=100.

		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