The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

Table 1

Simulation results for Example 1: the mean and standard deviations (in parentheses) of two different measures and the running times.

Model	Method	Sample size	Frobenius norm	Trace correlation	Runtime (second)
Model (18)	ADMM	100	0.1338 (0.0996)	0.9861 (0.0196)	62.3846
		200	0.0941 (0.0710)	0.9931 (0.0095)	152.3062
		400	0.0678 (0.0509)	0.9964 (0.0050)	213.2868
	Xia et al. [7]	100	0.1321 (0.0973)	0.9865 (0.0187)	64.2370
		200	0.0950 (0.0698)	0.9931 (0.0094)	161.7568
		400	0.0697 (0.0514)	0.9963 (0.0050)	216.0695
Model (19)	ADMM	100	0.0676 (0.0338)	0.9971 (0.0028)	76.1789
		200	0.0444 (0.0241)	0.9987 (0.0014)	184.7710
		400	0.0318 (0.0174)	0.9993 (0.0007)	242.7430
	Xia et al. [7]	100	0.0698 (0.0348)	0.9970 (0.0030)	76.3474
		200	0.0483 (0.0252)	0.9985 (0.0015)	185.15548
		400	0.0322 (0.0170)	0.9993 (0.0007)	245.4477