Table 1.

Cosine angle estimates of eigenvectors and PC scores based on 1000 simulations. “Angle” indicates the theoretical asymptotic cos (angle), “Estimate1” indicates the empirical cos(angle) estimator, ‘Estimate2” indicates the asymptotic cos(angle) estimator. For each estimator, each entry represents mean of 1, 000 simulation results with standard error in parentheses.

γ	n	PC 1			PC 2
		Angle	Angle Estimate1	Angle Estimate2	Angle	Angle Estimate1	Angle Estimate2
Eigenvectors
1	100	0.93	0.93(0.013)	0.91(0.027)	0.82	0.81(0.053)	0.80(0.052)
	200		0.93(0.009)	0.92(0.014)		0.81(0.030)	0.81(0.032)
20	100	0.70	0.69(0.037)	0.70(0.031)	0.51	0.50(0.053)	0.50(0.058)
	200		0.69(0.023)	0.70(0.022)		0.51(0.036)	0.51(0.041)
100	100	0.53	0.53(0.034)	0.53(0.031)	0.37	0.35(0.043)	0.35(0.047)
	200		0.53(0.024)	0.53(0.024)		0.36(0.029)	0.36(0.033)
500	100	0.38	0.38(0.029)	0.38(0.028)	0.25	0.24(0.033)	0.24(0.037)
	200		0.38(0.020)	0.38(0.020)		0.25(0.021)	0.25(0.024)
PC Scores
1	100	0.99	0.99(0.004)	0.98(0.016)	0.94	0.93(0.036)	0.91(0.048)
	200		0.99(0.003)	0.99(0.006)		0.94(0.019)	0.93(0.024)
20	100	0.98	0.97(0.083)	0.98(0.008)	0.89	0.86(0.105)	0.87(0.055)
	200		0.97(0.055)	0.98(0.005)		0.88(0.073)	0.88(0.036)
100	100	0.97	0.97(0.079)	0.97(0.009)	0.88	0.85(0.109)	0.86(0.060)
	200		0.97(0.058)	0.97(0.006)		0.86(0.076)	0.87(0.039)
500	100	0.97	0.96(0.084)	0.97(0.010)	0.87	0.83(0.117)	0.84(0.069)
	200		0.96(0.058)	0.97(0.007)		0.86(0.076)	0.86(0.038)