Table 2.

Average MSEs over 100 simulations for estimating σ, the eigenvalues and the principal scores under various signal-to-noise ratios. The values are augmented 100 times for better presentation.

σ	MSEλX (10−2)				MSEλU (10−2)				MSEλW (10−2)
	${\lambda }_1^X$	${\lambda }_2^X$	${\lambda }_3^X$	${\lambda }_4^X$	${\lambda }_1^U$	${\lambda }_2^U$	${\lambda }_3^U$	${\lambda }_4^U$	${\lambda }_1^W$	${\lambda }_2^W$	${\lambda }_3^W$	${\lambda }_4^W$
0	3.2	0.9	0.2	0.1	1.2	0.3	0.1	0.02	0.2	0.1	0.01	2E-3
0.1	4.5	0.9	0.2	0.1	1.3	0.7	0.2	0.2	0.2	0.1	0.02	8E-3
0.5	5	1.6	1.4	0.4	1.3	9.3	3.2	1.0	6.5	6.7	3.5	2.7
1	8	5	2.8	0.6	2	15.5	4.1	0.8	102	101	33.6	21.7

${\mathrm{MSE}}_{\widehat{\sigma }}\left({10}^{-2}\right)$	MSEξ (10−2)				MSEθ (10−2)				MSEζ (10−2)
	ξ 1	ξ 2	ξ 3	ξ 4	θ 1	θ 2	θ 3	θ 4	ζ 1	ζ 2	ζ 3	ζ 4
2E-17	14.7	11.2	7.6	136	120	4.5	2.5	2	20.2	8.1	0.5	2.6
3E-8	42.7	18.2	5.5	34.7	305	5.6	3.2	2	280	30.5	9.9	15.8
4E-7	267	129.2	17.7	22.2	1660	22.8	12	19.1	1623	226	161	102
1E-6	370	159	36.1	22.5	1657	50.1	58.3	31.7	1677	466	245	153