Table 3.

Performance measures for L ₀, L ₁, SCAD, and MC+ regularized regressions with cross validation and λ = Max⁡⁡{λ _MSE, λ _SS} over 100 simulations and the sample size of n = 100, and m = 1000, where values in the parenthesis are the standard deviations. # SF: number of average selected features; MSE: average mean squared error; $‖\widehat{\theta }-\theta ‖$: average absolute bias when comparing true and estimated parameters.

	Measures	r = 0	r = 0.3	r = 0.6
L 0	# SF	3 (±0)	2.9 (±0.47)	2 (±0.73)
	$\Vert \widehat{\theta }-\theta \Vert$	0.14 (±0.09)	0.39 (±0.63)	1.69 (±1.25)
	Test MSE	1.14 (±0.34)	1.59 (±1.3)	2.8 (±1.72)
	# true model	100/100	78/100	23/100
L 1	# SF	24 (±18.4)	31.3 (±20.7)	36.7 (±16.5)
	$\Vert \widehat{\theta }-\theta \Vert$	0.57 (±0.11)	0.73 (±0.13)	1.14 (±0.25)
	Test MSE	1.50 (±0.25)	1.63 (±0.29)	1.92 (±0.41)
	# true model	0/100	0/100	0/100
SCAD	# SF	106.8 (±110.6)	73 (±111)	56.2 (±62.4)
	$\Vert \widehat{\theta }-\theta \Vert$	0.62 (±0.13)	0.72 (±0.14)	1.13 (±0.26)
	Test MSE	1.32 (±0.27)	1.54 (±0.27)	2.04 (±0.51)
	# true model	0/100	0/100	0/100
MC+	# SF	60.3 (±38.6)	70.5 (±26.0)	78.73 (±16.5)
	$\Vert \widehat{\theta }-\theta \Vert$	0.56 (±0.14)	0.66 (±0.12)	0.78 (±0.17)
	Test MSE	1.25 (±0.21)	1.31 (±0.27)	1.46 (±0.27)
	# true model	0/100	0/100	0/100