Table 2.
Sample and predicted principal component scores based on 500 simulations. UltraHigh and Finite γ present theoretical asymptotic values from the ultra-high dimensional and the finite γ regimes, respectively. Observed presents the median of the estimates, with the interquartile range in parentheses.
| γp | Type | Principal Component 1 | Principal Component 2 | |||
|---|---|---|---|---|---|---|
| Moderate Spike | Very Large Spike | Moderate Spike | Very Large Spike | |||
| Principal Component Scores | 500 | Ultra-High | 1.00 | 1.00 | 1.00 | 1.00 |
| Finite γ | 1.00 | 1.00 | 1.00 | 1.00 | ||
| Observed | 0.99(0.042) | 0.99(0.043) | 0.97(0.090) | 0.97(0.087) | ||
| 2000 | Ultra-High | 1.00 | 1.00 | 1.00 | 1.00 | |
| Finite γ | 1.00 | 1.00 | 1.00 | 1.00 | ||
| Observed | 0.99(0.039) | 0.99(0.038) | 0.97(0.078) | 0.97(0.079) | ||
| Shrinkage Factors | 500 | Ultra-High | 0.50 | 0.96 | 0.41 | 0.94 |
| Finite γ | 0.50 | 0.96 | 0.41 | 0.94 | ||
| Observed | 0.49(0.045) | 0.93(0.120) | 0.42(0.046) | 0.97(0.122) | ||
| 2000 | Ultra-High | 0.50 | 0.98 | 0.41 | 0.97 | |
| Finite γ | 0.50 | 0.98 | 0.41 | 0.97 | ||
| Observed | 0.49(0.045) | 0.95(0.127) | 0.42(0.041) | 1.00(0.118) | ||