Group Identification and Variable Selection in Quantile Regression

Table 4

ME, SA, GA, and SGA results of Example 4 for n=100.

		Criterion	Ridge	QR-	QR-	QR-	QR-	QR-PACS
			QR	LASSO	SCAD	adaptive LASSO	elastic-net
=1	0.10	ME(S.E)	0.1380(0.0193)	0.1149(0.0195)	0.0939(0.0165)	0.0937(0.0153)	0.0832(0.0130)	0.0560(0.0105)
		SA	0	57	79	79	82	78
		GA	0	0	0	0	0	86
		SGA	0	0	0	0	0	71
	0.50	ME(S.E)	0.1132(0.0069)	0.0816(0.0062)	0.0672(0.0060)	0.0672(0.0056)	0.0568(0.0062)	0.0369(0.0036)
		SA	0	62	81	81	85	80
		GA	0	0	0	0	0	86
		SGA	0	0	0	0	0	72
	0.75	ME(S.E)	0.1280(0.0178)	0.1056(0.0171)	0.0873(0.0164)	0.0872(0.0149)	0.0764(0.0119)	0.0481(0.0088)
		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)	0.1495(0.0200)	0.1270(0.0197)	0.1016(0.0169)	0.1008(0.0154)	0.0970(0.0120)	0.0639(0.0100)
		SA	0	57	78	78	81	77
		GA	0	0	0	0	0	84
		SGA	0	0	0	0	0	70
	0.50	ME(S.E)	0.1239(0.0072)	0.0928(0.0064)	0.0859(0.0060)	0.0738(0.0054)	0.0730(0.0051)	0.0458(0.0029)
		SA	0	62	80	80	83	79
		GA	0	0	0	0	0	85
		SGA	0	0	0	07	0	70
	0.75	ME(S.E)	0.1391(0.0181)	0.1182(0.0167)	0.0953(0.0163)	0.0941(0.0158)	0.0921(0.0106)	0.0559(0.0081)
		SA	0	60	79	80	83	78
		GA	0	0	0	0	0	85
		SGA	0	0	0	0	0	70