Research Article
A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications
Table 2
Estimated MSE when
n = 30,
, and
ρ = 0.90 and 0.99.
| n = 30 | 0.9 | 0.99 | Sigma | k = d | OLS | Ridge | Liu | New est | OLS | Ridge | Liu | New est |
| 1 | 0.1 | 1.154 | 1.012 | 0.532 | 0.883 | 12.774 | 4.155 | 0.857 | 1.128 | | 0.2 | | 0.899 | 0.583 | 0.691 | | 2.339 | 1.388 | 1.946 | | 0.3 | | 0.809 | 0.638 | 0.555 | | 1.603 | 2.117 | 3.278 | | 0.4 | | 0.736 | 0.697 | 0.459 | | 1.214 | 3.045 | 4.416 | | 0.5 | | 0.675 | 0.762 | 0.392 | | 0.978 | 4.170 | 5.340 | | 0.6 | | 0.625 | 0.831 | 0.346 | | 0.821 | 5.495 | 6.097 | | 0.7 | | 0.582 | 0.905 | 0.317 | | 0.712 | 7.017 | 6.725 | | 0.8 | | 0.545 | 0.983 | 0.299 | | 0.631 | 8.738 | 7.255 | | 0.9 | | 0.514 | 1.066 | 0.291 | | 0.571 | 10.656 | 7.708 | | 1 | | 0.487 | 1.154 | 0.289 | | 0.524 | 12.774 | 8.100 |
| 5 | 0.1 | 28.461 | 24.840 | 12.067 | 21.501 | 319.335 | 102.389 | 17.451 | 23.383 | | 0.2 | | 21.945 | 13.492 | 16.402 | | 56.008 | 31.445 | 40.368 | | 0.3 | | 19.588 | 15.017 | 12.625 | | 36.978 | 50.327 | 71.447 | | 0.4 | | 17.641 | 16.640 | 9.805 | | 26.816 | 74.095 | 98.322 | | 0.5 | | 16.010 | 18.362 | 7.690 | | 20.580 | 102.751 | 120.269 | | 0.6 | | 14.627 | 20.184 | 6.104 | | 16.415 | 136.293 | 138.268 | | 0.7 | | 13.442 | 22.105 | 4.917 | | 13.467 | 174.723 | 153.240 | | 0.8 | | 12.418 | 24.124 | 4.036 | | 11.293 | 218.040 | 165.880 | | 0.9 | | 11.526 | 26.243 | 3.393 | | 9.637 | 266.244 | 176.695 | | 1 | | 10.741 | 28.461 | 2.935 | | 8.343 | 319.335 | 186.058 |
| 10 | 0.1 | 113.841 | 99.331 | 48.088 | 85.947 | 1277.429 | 409.249 | 69.149 | 92.868 | | 0.2 | | 87.726 | 53.814 | 65.494 | | 223.571 | 125.195 | 160.554 | | 0.3 | | 78.277 | 59.935 | 50.326 | | 147.369 | 200.793 | 284.749 | | 0.4 | | 70.466 | 66.450 | 38.986 | | 106.666 | 295.943 | 392.184 | | 0.5 | | 63.919 | 73.361 | 30.469 | | 81.687 | 410.644 | 479.940 | | 0.6 | | 58.368 | 80.667 | 24.064 | | 64.998 | 544.898 | 551.916 | | 0.7 | | 53.612 | 88.368 | 19.262 | | 53.189 | 698.703 | 611.794 | | 0.8 | | 49.498 | 96.464 | 15.687 | | 44.476 | 872.060 | 662.350 | | 0.9 | | 45.910 | 104.955 | 13.064 | | 37.839 | 1064.960 | 705.611 | | 1 | | 42.758 | 113.841 | 11.182 | | 32.655 | 1277.429 | 743.065 |
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