Group Identification and Variable Selection in Quantile Regression

Table 2

ME, SA, GA, and SGA results of Example 2 for n=100.

		Criterion	Ridge	QR-	QR-	QR-	QR-	QR-PACS
			QR	LASSO	SCAD	adaptive LASSO	elastic-net
=1	0.10	ME(S.E)	0.1170(0.0201)	0.0848(0.0195)	0.0696(0.0177)	0.0665(0.0165)	0.0639(0.0106)	0.0445(0.0101)
		SA	0	60	78	78	84	78
		NG	100	100	100	100	100	100
		SNG	0	69	70	70	78	69
	0.50	ME(S.E)	0.0857(0.0075)	0.0538(0.0068)	0.0456(0.0062)	0.0439(0.0057)	0.0421(0.0055)	0.0156(0.0035)
		SA	0	63	81	81	84	79
		NG	100	100	100	100	100	100
		SNG	0	70	71	71	80	70
	0.75	ME(S.E)	0.1155(0.0185)	0.0841(0.0179)	0.0681(0.0161)	0.0679(0.0155)	0.0630(0.0111)	0.0437(0.0090)
		SA	0	61	80	81	84	79
		NG	100	100	100	100	100	100
		SNG	0	70	70	71	79	70
=3	0.10	ME(S.E)	0.1275(0.0213)	0.0968(0.0199)	0.0788(0.0185)	0.0745(0.0183)	0.0728(0.0106)	0.0419(0.0117)
		SA	0	57	77	77	83	77
		NG	100	100	100	100	100	100
		SNG	0	67	69	69	76	67
	0.50	ME(S.E)	0.0876(0.0078)	0.0549(0.0072)	0.0464(0.0064)	0.0447(0.0062)	0.0430(0.0060)	0.0156(0.0040)
		SA	0	63	80	80	83	79
		NG	100	100	100	100	100	100
		SNG	0	69	70	70	79	69
	0.75	ME(S.E)	0.1164(0.0190)	0.0850(0.0187)	0.0692(0.0170)	0.0688(0.0162)	0.0639(0.0120)	0.0446(0.0098)
		SA	0	60	79	80	84	79
		NG	100	100	100	100	100	100
		SNG	0	69	70	70	78	69