Table 5.
Simulation results under the high dimensional scenario (30 × 15 × 15) when the true model is rank-2. In the Sparsity column, the numbers in parentheses indicate the number of non-zero variables in each dimension. “Cor” is the correlation between the estimated linear hyperplane and the true hyperplane. “Mis” is the average misclassification rate. “TP” is the true positive rate, i.e., the proportion of non-zero coefficients that are correctly estimated to be non-zero.“TN” is the true negative rate, i.e., the proportion of zero coefficients that are correctly estimated to be zero. The margins of error (2* standard errors across 200 replicates) for each statistic are also listed following the ± symbol.
| N | Sparsity | Methods | Cor | Mis | TP | TN |
|---|---|---|---|---|---|---|
| 40 | More (5 × 5 × 5) | M-SDWD (R=2) | 0.833±0.020 | 0.027±0.011 | 0.714±0.038 | 0.761±0.043 |
| M-SDWD (λ1 = 0, R=2) | 0.747±0.025 | 0.040±0.013 | 1.000±0.000 | 0.000±0.000 | ||
| M-SDWD (R=1) | 0.779±0.025 | 0.035±0.014 | 0.678±0.039 | 0.716±0.050 | ||
| M-SDWD (λ1 = 0, R=1) | 0.745±0.026 | 0.043±0.015 | 1.000±0.000 | 0.000±0.000 | ||
| M-DWD | 0.736±0.033 | 0.055±0.019 | 1.000±0.000 | 0.000±0.000 | ||
| Full SDWD | 0.591±0.024 | 0.071±0.015 | 0.150±0.013 | 0.984±0.007 | ||
| Less (10 × 15 × 15) | M-SDWD (R=2) | 0.984±0.003 | 0.000±0.000 | 0.942±0.016 | 0.402±0.060 | |
| M-SDWD (λ1 = 0, R=2) | 0.990±0.002 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| M-SDWD (R=1) | 0.813±0.011 | 0.000±0.000 | 0.840±0.029 | 0.488±0.062 | ||
| M-SDWD (λ1 = 0, R=1) | 0.821±0.010 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| M-DWD | 0.786±0.016 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| Full SDWD | 0.750±0.009 | 0.000±0.000 | 0.239±0.018 | 0.937±0.012 | ||
| No (30 × 15 × 15) | M-SDWD (R=2) | 0.996±0.000 | 0.000±0.000 | 1.000±0.000 | - | |
| M-SDWD (λ1 = 0, R=2) | 0.996±0.000 | 0.000±0.000 | 1.000±0.000 | - | ||
| M-SDWD (R=1) | 0.790±0.012 | 0.000±0.000 | 0.836±0.033 | - | ||
| M-SDWD (λ1 = 0, R=1) | 0.799±0.010 | 0.000±0.000 | 1.000±0.000 | - | ||
| M-DWD | 0.763±0.016 | 0.000±0.000 | 1.000±0.000 | - | ||
| Full SDWD | 0.784±0.006 | 0.000±0.000 | 0.399±0.036 | - | ||
| 100 | More (5 × 5 × 5) | M-SDWD (R=2) | 0.925±0.010 | 0.012±0.004 | 0.841±0.026 | 0.754±0.041 |
| M-SDWD (λ1 = 0, R=2) | 0.889±0.011 | 0.016±0.005 | 1.000±0.000 | 0.000±0.000 | ||
| M-SDWD (R=1) | 0.853±0.012 | 0.015±0.004 | 0.738±0.031 | 0.818±0.039 | ||
| M-SDWD (λ1 = 0, R=1) | 0.829±0.014 | 0.019±0.005 | 1.000±0.000 | 0.000±0.000 | ||
| M-DWD | 0.825±0.020 | 0.027±0.010 | 1.000±0.000 | 0.000±0.000 | ||
| Full SDWD | 0.797±0.014 | 0.026±0.007 | 0.236±0.016 | 0.992±0.002 | ||
| Less (10 × 15 × 15) | M-SDWD (R=2) | 0.992±0.001 | 0.000±0.000 | 0.958±0.012 | 0.456±0.061 | |
| M-SDWD (λ1 = 0, R=2) | 0.996±0.000 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| M-SDWD (R=1) | 0.807±0.010 | 0.000±0.000 | 0.871±0.024 | 0.526±0.062 | ||
| M-SDWD (λ1 = 0, R=1) | 0.807±0.010 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| M-DWD | 0.797±0.012 | 0.000±0.000 | 1.000±0.000 | 0.000±0.000 | ||
| Full SDWD | 0.856±0.005 | 0.000±0.000 | 0.346±0.019 | 0.935±0.012 | ||
| No (30 × 15 × 15) | M-SDWD (R=2) | 0.998±0.000 | 0.000±0.000 | 1.000±0.000 | - | |
| M-SDWD (λ1 = 0, R=2) | 0.998±0.000 | 0.000±0.000 | 1.000±0.000 | - | ||
| M-SDWD (R=1) | 0.786±0.009 | 0.000±0.000 | 0.908±0.023 | - | ||
| M-SDWD (λ1 = 0, R=1) | 0.790±0.009 | 0.000±0.000 | 1.000±0.000 | - | ||
| M-DWD | 0.758±0.014 | 0.000±0.000 | 1.000±0.000 | - | ||
| Full SDWD | 0.871±0.004 | 0.000±0.000 | 0.466±0.029 | - |