Table 1.

The MMMS and RSD (in parenthesis) of the simulated examples for linear and logistic regression from simulation model I with n = 500 when p = 1000 and p = 10000. PC=0 refers to the marginal screening in Fan and Lv (2008).

PCs	Variance	SIS-PCA-MLR	SIS-PCA-MMLE	SIS-PCA-MLR	SIS-PCA-MMLE
Setting 1, linear model with p = 1000
		s = 6, β★ = (0.3,−0.3, 0.3, …)T		s = 12, β★ = (3, 4, 3, …)T
0	0	13(35)	13(35)	101(96)	101(96)
1	41.5%	7(3)	7(4)	12(0)	12(0)
3	42.2%	7(3)	7(4)	12(0)	12(0)
5	42.8%	7(3)	7(3)	12(0)	12(0)
10	44.4%	7(4)	7(4)	12(0)	12(0)
30	50.2%	8(5)	8(5)	12(0)	12(0)
50	55.4%	11(8)	10(8)	12(0)	12(0)
100	66.4%	19.5(32)	19(31)	12(1)	12(1)
Setting 2, logistic regression with p = 1000
		s = 6, β★ = (0.7,−0.7, 0.7, …)T		s = 8, β★ = (3, 4, 3, …)T
0	0	14(26)	14(26)	70.5(80)	64(82)
1	41.7%	7(3)	7(3)	21(31)	23(28)
3	42.4%	7(3)	7(3)	22.5(31)	24(30)
5	43.0%	7(4)	7(3)	25(29)	26(32)
10	44.6%	7(4)	8(4)	24(38)	27(38)
30	50.4%	8(7)	8(7)	38(49)	37(46)
50	55.5%	10(10)	10.5(10)	58(72)	60(80)
100	66.5%	22(34)	24.5(34)	532(460)	414(347)
Setting 3, linear model with p = 10000
		s = 6, β★ = (0.3,−0.3, 0.3, …)T		s = 12, β★ = (3, 4, 3, 4, …)T
0	0	90.5(501)	90.5(501)	830.5(924)	830.5(924)
1	40.3%	14.5(37)	14(35)	12(1)	12(1)
3	40.6%	15(35)	14(34)	12(1)	12(1)
5	41.0%	15(30)	14(29)	12(1)	12(1)
10	41.9%	16.5(36)	15(35)	12(1)	12(1)
30	45.2%	27(49)	25.5(45)	12(1)	12(1)
50	48.5%	36.5(100)	36.5(95)	12(2)	12(2)
100	56.1%	70.5(171)	67.5(170)	14(8)	14(7)
Setting 4, logistic regression with p = 10000
		s = 6, β★ = (0.7,−0.7, 0.7, …)T		s = 8, β★ = (3, 4, 3, …)T
0	0	112(365)	112(366)	641(742)	609.5(731)
1	41.5%	15(30)	16(29)	142(339)	146(354)
3	41.8%	16(32)	17(32)	149.5(372)	160(351)
5	42.2%	15(37)	17(36)	157(392)	168.5(394)
10	43.0%	16.5(35)	17(37)	154(351)	160(367)
30	46.3%	28(51)	26(50)	259(663)	259(646)
50	49.5%	36(68)	34.5(71)	410.5(834)	455(879)
100	57.0%	78.5(206)	80.5(238)	6837(6317)	2570(3513)