Group Identification and Variable Selection in Quantile Regression

Table 1

ME, SA, GA, and SGA results of Example 1 for n=100.

		Criterion	Ridge	QR-	QR-	QR-	QR-	QR-PACS
			QR	LASSO	SCAD	adaptive LASSO	elastic-net
=1	0.10	ME(S.E)	0.1144(0.0176)	0.0834(0.0182)	0.0684(0.0165)	0.0673(0.0153)	0.0623(0.0112)	0.0432(0.0093)
		SA	0	62	79	80	87	79
		GA	0	0	0	0	0	88
		SGA	0	0	0	0	0	72
	0.50	ME(S.E)	0.0832(0.0056)	0.0524(0.0065)	0.0443(0.0056)	0.0431(0.0050)	0.0404(0.0041)	0.0143(0.0020)
		SA	0	64	81	82	86	80
		GA	0	0	0	0	0	89
		SGA	0	0	0	0	0	73
	0.75	ME(S.E)	0.1140(0.0173)	0.0829(0.0177)	0.0672(0.0150)	0.0668(0.0146)	0.0619(0.0105)	0.0429(0.0082)
		SA	0	63	81	81	88	80
		GA	0	0	0	0	0	89
		SGA	0	0	0	0	0	72
=3	0.10	ME(S.E)	0.1471(0.0183)	0.1168(0.0188)	0.1062(0.0162)	0.1056(0.0162)	0.0953(0.0120)	0.0755(0.0106)
		SA	0	59	77	77	84	77
		GA	0	0	0	0	0	86
		SGA	0	0	0	0	0	70
	0.50	ME(S.E)	0.1153(0.0066)	0.0855(0.0071)	0.0763(0.0060)	0.0756(0.0060)	0.0730(0.0049)	0.0473(0.0034)
		SA	0	61	80	80	83	78
		GA	0	0	0	0	0	87
		SGA	0	0	0	0	0	71
	0.75	ME(S.E)	0.1466(0.0179)	0.1161(0.0185)	0.1056(0.0161)	0.1044(0.0158)	0.0945(0.0117)	0.0744(0.0099)
		SA	0	61	79	79	85	78
		GA	0	0	0	0	0	87
		SGA	0	0	0	0	0	70