Research Article
A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications
Table 5
Estimated MSE when
n = 30,
, and
ρ = 0.70 and 0.80.
| n = 30 | 0.7 | 0.8 | Sigma | k = d | OLS | Ridge | Liu | New ridge | OLS | Ridge | Liu | New ridge |
| 1 | 0.1 | 0.838 | 0.811 | 0.651 | 0.785 | 1.239 | 1.179 | 0.859 | 1.121 | | 0.2 | | 0.786 | 0.670 | 0.737 | | 1.124 | 0.895 | 1.018 | | 0.3 | | 0.763 | 0.689 | 0.694 | | 1.074 | 0.933 | 0.928 | | 0.4 | | 0.741 | 0.709 | 0.654 | | 1.029 | 0.973 | 0.850 | | 0.5 | | 0.720 | 0.729 | 0.618 | | 0.987 | 1.014 | 0.781 | | 0.6 | | 0.701 | 0.750 | 0.586 | | 0.949 | 1.056 | 0.721 | | 0.7 | | 0.682 | 0.771 | 0.556 | | 0.914 | 1.100 | 0.669 | | 0.8 | | 0.665 | 0.793 | 0.529 | | 0.881 | 1.145 | 0.623 | | 0.9 | | 0.649 | 0.815 | 0.505 | | 0.851 | 1.191 | 0.583 | | 1 | | 0.633 | 0.838 | 0.484 | | 0.823 | 1.239 | 0.549 |
| 5 | 0.1 | 20.955 | 20.275 | 16.063 | 19.608 | 30.981 | 29.455 | 21.084 | 27.975 | | 0.2 | | 19.633 | 16.568 | 18.362 | | 28.060 | 22.071 | 25.314 | | 0.3 | | 19.026 | 17.083 | 17.208 | | 26.780 | 23.086 | 22.951 | | 0.4 | | 18.452 | 17.607 | 16.139 | | 25.602 | 24.130 | 20.845 | | 0.5 | | 17.908 | 18.141 | 15.147 | | 24.513 | 25.201 | 18.963 | | 0.6 | | 17.391 | 18.685 | 14.226 | | 23.506 | 26.301 | 17.279 | | 0.7 | | 16.901 | 19.238 | 13.369 | | 22.570 | 27.429 | 15.767 | | 0.8 | | 16.435 | 19.801 | 12.572 | | 21.699 | 28.585 | 14.408 | | 0.9 | | 15.990 | 20.373 | 11.829 | | 20.885 | 29.769 | 13.185 | | 1 | | 15.567 | 20.955 | 11.137 | | 20.125 | 30.981 | 12.081 |
| 10 | 0.1 | 83.821 | 81.095 | 64.205 | 78.423 | 123.923 | 117.811 | 84.259 | 111.887 | | 0.2 | | 78.523 | 66.233 | 73.429 | | 112.224 | 88.219 | 101.225 | | 0.3 | | 76.091 | 68.299 | 68.804 | | 107.097 | 92.291 | 91.749 | | 0.4 | | 73.789 | 70.403 | 64.513 | | 102.375 | 96.475 | 83.301 | | 0.5 | | 71.608 | 72.545 | 60.530 | | 98.014 | 100.770 | 75.750 | | 0.6 | | 69.537 | 74.725 | 56.827 | | 93.973 | 105.177 | 68.983 | | 0.7 | | 67.569 | 76.942 | 53.382 | | 90.220 | 109.696 | 62.908 | | 0.8 | | 65.698 | 79.197 | 50.173 | | 86.725 | 114.327 | 57.441 | | 0.9 | | 63.915 | 81.490 | 47.182 | | 83.463 | 119.069 | 52.515 | | 1 | | 62.215 | 83.821 | 44.392 | | 80.411 | 123.923 | 48.069 |
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