Table 3.
For m = 50, displayed are the distributions of the number of selected principal components p̂ for all methods and across Scenarios I-IV. The true number of principal components is 3.
| Scenario | Method | p̂ = 1 | p̂ = 2 | p̂ = 3 | p̂ = 4 | p̂ ≥ 5 |
|---|---|---|---|---|---|---|
| I | AICPACE | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 |
| AIC | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| BIC | 0.000 | 0.000 | 0.830 | 0.150 | 0.020 | |
| PCp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| ICp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| II | AICPACE | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 |
| AIC | 0.000 | 0.000 | 0.630 | 0.320 | 0.050 | |
| BIC | 0.000 | 0.000 | 0.795 | 0.185 | 0.020 | |
| PCp1 | 0.000 | 0.000 | 0.955 | 0.045 | 0.000 | |
| ICp1 | 0.000 | 0.000 | 0.945 | 0.055 | 0.000 | |
| III | AICPACE | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 |
| AIC | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| BIC | 0.000 | 0.000 | 0.775 | 0.200 | 0.025 | |
| PCp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| ICp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| IV | AICPACE | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 |
| AIC | 0.000 | 0.000 | 0.945 | 0.055 | 0.000 | |
| BIC | 0.000 | 0.000 | 0.835 | 0.140 | 0.025 | |
| PCp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | |
| ICp1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 |