Table 2.
When m = 10, 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 | 0.005 | 0.980 | 0.015 | 0.000 | |
| BIC | 0.000 | 0.040 | 0.670 | 0.255 | 0.035 | |
| PCp1 | 0.000 | 0.040 | 0.955 | 0.000 | 0.005 | |
| ICp1 | 0.000 | 0.005 | 0.985 | 0.010 | 0.000 | |
| II | AICPACE | 0.000 | 0.000 | 0.000 | 0.005 | 0.995 |
| AIC | 0.000 | 0.000 | 0.710 | 0.260 | 0.030 | |
| BIC | 0.000 | 0.170 | 0.665 | 0.135 | 0.030 | |
| PCp1 | 0.000 | 0.000 | 0.570 | 0.355 | 0.075 | |
| ICp1 | 0.000 | 0.000 | 0.805 | 0.185 | 0.010 | |
| III | AICPACE | 0.000 | 0.015 | 0.000 | 0.000 | 0.985 |
| AIC | 0.000 | 0.000 | 0.580 | 0.400 | 0.020 | |
| BIC | 0.005 | 0.035 | 0.770 | 0.145 | 0.045 | |
| PCp1 | 0.000 | 0.000 | 0.965 | 0.030 | 0.005 | |
| ICp1 | 0.000 | 0.000 | 0.665 | 0.320 | 0.015 | |
| IV | AICPACE | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 |
| AIC | 0.000 | 0.000 | 0.830 | 0.150 | 0.020 | |
| BIC | 0.010 | 0.005 | 0.775 | 0.190 | 0.020 | |
| PCp1 | 0.000 | 0.000 | 0.920 | 0.045 | 0.035 | |
| ICp1 | 0.000 | 0.000 | 0.900 | 0.085 | 0.015 |