Table 3:

Performance of proposed algorithms for PQR when p = 1000 and n = 30000.

n = 30000, p = 1000	$\tau$	${\Vert \widehat{\mathit{\beta }}-\mathit{\beta }\Vert }_1$	P1	P2	Size
FS-QRADMM-CD (Lasso)	0.3	0.031 (0.0004)	100%	100%	5.06 (0.003)
	0.5	0.020 (0.0004)	100%	0.4%	4.04 (0.003)
	0.7	0.029 (0.0004)	100%	100%	5.06 (0.003)
FS-QRADMM-prox (Lasso)	0.3	0.029 (0.0003)	100%	100%	5.05 (0.003)
	0.5	0.020 (0.0003)	100%	0.5%	4.03 (0.002)
	0.7	0.029 (0.0003)	100%	100%	5.05 (0.003)
qradmm(Lasso)	0.3	0.030 (0.0004)	100%	100%	5.08 (0.003)
	0.5	0.023 (0.0003)	100%	0.6%	4.05 (0.004)
	0.7	0.029 (0.0004)	100%	100%	5.04 (0.004)
rqPen(Lasso)	The algorithm runs out of memory for τ = 0.3, 0.5, 0.7
hqReg(Lasso)	0.3	0.040 (0.0008)	100%	100%	6.06 (0.09)
	0.5	0.020 (0.0002)	100%	1%	4.60 (0.07)
	0.7	0.040 (0.0008)	100%	51.6%	5.90 (0.09)
Conquer(Lasso)	0.3	0.066 (0.0009)	100%	100%	5.23 (0.04)
	0.5	0.020 (0.0003)	100%	0%	4.11 (0.04)
	0.7	0.065 (0.0009)	100%	100%	5.25 (0.05)
FS-QRADMM-CD (TS-SCAD)	0.3	0.012 (0.0005)	100%	100%	5.00 (0.00)
	0.5	0.004 (0.0002)	100%	0.2%	4.00 (0.00)
	0.7	0.013 (0.0004)	100%	100%	5.00 (0.00)
FS-QRADMM-prox (TS-SCAD)	0.3	0.011 (0.0003)	100%	100%	5.00 (0.00)
	0.5	0.004 (0.0002)	100%	0%	4.00 (0.00)
	0.7	0.012 (0.0003)	100%	100%	5.00 (0.00)
qradmm (TS-SCAD) (TS-SCAD)	0.3	0.012 (0.0004)	100%	100%	5.00 (0.00)
	0.5	0.004 (0.0003)	100%	0%	4.00 (0.00)
	0.7	0.011 (0.0005)	100%	100%	5.00 (0.00)
rqPen (TS-SCAD)	The algorithm runs out of memory for τ = 0.3, 0.5, 0.7
Conquer(SCAD)	0.3	0.028 (0.0008)	100%	100%	5.15 (0.039)
	0.5	0.005 (0.0002)	100%	1%	4.45 (0.061)
	0.7	0.029 (0.0008)	100%	100%	5.14 (0.037)