Group Identification and Variable Selection in Quantile Regression

Table 5

ME, SA, GA, and SGA results of Example 5 for n=100.

		Criterion	Ridge	QR-	QR-	QR-	QR-	QR-PACS
			QR	LASSO	SCAD	adaptive LASSO	elastic-net
=1	0.10	ME(S.E)	0.1330(0.0161)	0.1106(0.0168)	0.0914(0.0154)	0.0910(0.0142)	0.0818(0.0122)	0.0548(0.0981)
		SA	0	58	79	79	84	79
		GA	0	0	0	0	0	87
		SGA	0	0	0	0	0	72
	0.50	ME(S.E)	0.1119(0.0061)	0.0807(0.0053)	0.0666(0.0054)	0.0663(0.0051)	0.0561(0.0054)	0.0358(0.0031)
		SA	0	63	82	82	86	81
		GA	0	0	0	0	0	87
		SGA	0	0	0	0	0	73
	0.75	ME(S.E)	0.1274(0.0169)	0.1048(0.0162)	0.0867(0.0157)	0.0865(0.0143)	0.0756(0.0109)	0.0476(0.0079)
		SA	0	62	81	81	84	79
		GA	0	0	0	0	0	87
		SGA	0	0	0	0	0	72
=3	0.10	ME(S.E)	0.1486(0.0188)	0.1260(0.0189)	0.1001(0.0156)	0.1000(0.0148)	0.0960(0.0110)	0.0625(0.0088)
		SA	0	57	77	77	81	78
		GA	0	0	0	0	0	84
		SGA	0	0	0	0	0	70
	0.50	ME(S.E)	0.1227(0.0069)	0.0922(0.0059)	0.0850(0.0053)	0.0731(0.0047)	0.0724(0.0045)	0.0445(0.0020)
		SA	0	63	80	80	83	80
		GA	0	0	0	0	0	85
		SGA	0	0	0	0	0	70
	0.75	ME(S.E)	0.1385(0.0177)	0.1172(0.0154)	0.0940(0.0154)	0.0935(0.0151)	0.0926(0.0100)	0.0552(0.0075)
		SA	0	60	80	80	83	79
		GA	0	0	0	0	0	85
		SGA	0	0	0	0	0	70