Research Article
Modified One-Parameter Liu Estimator for the Linear Regression Model
| | | 0.7 | 0.8 | 0.9 | 0.99 | | OLS | Ridge | Liu | MLiu | OLS | Ridge | Liu | MLiu | OLS | Ridge | Liu | MLiu | OLS | Ridge | Liu | MLiu |
| 1 | 0.1 | 0.3621 | 0.3517 | 0.2909 | 0.2782 | 0.5473 | 0.5186 | 0.3750 | 0.3461 | 1.1540 | 1.0117 | 0.5323 | 0.4458 | 12.774 | 4.1554 | 0.8567 | 0.3894 | 0.2 | 0.3621 | 0.3420 | 0.2977 | 0.2722 | 0.5473 | 0.4929 | 0.3908 | 0.3329 | 1.1540 | 0.8995 | 0.5826 | 0.4096 | 12.774 | 2.3395 | 1.3877 | 0.4531 | 0.3 | 0.3621 | 0.3329 | 0.3047 | 0.2666 | 0.5473 | 0.4699 | 0.4073 | 0.3206 | 1.1540 | 0.8094 | 0.6376 | 0.3781 | 12.774 | 1.6033 | 2.1170 | 0.7151 | 0.4 | 0.3621 | 0.3245 | 0.3121 | 0.2612 | 0.5473 | 0.4493 | 0.4248 | 0.3092 | 1.1540 | 0.736 | 0.6973 | 0.3513 | 12.774 | 1.2143 | 3.0446 | 1.1753 | 0.5 | 0.3621 | 0.3167 | 0.3197 | 0.2561 | 0.5473 | 0.4306 | 0.4431 | 0.2985 | 1.1540 | 0.6754 | 0.7617 | 0.3292 | 12.774 | 0.9779 | 4.1705 | 1.8339 | 0.6 | 0.3621 | 0.3093 | 0.3276 | 0.2513 | 0.5473 | 0.4137 | 0.4622 | 0.2888 | 1.1540 | 0.6247 | 0.8307 | 0.3117 | 12.774 | 0.8214 | 5.4946 | 2.6906 | 0.7 | 0.3621 | 0.3025 | 0.3358 | 0.2468 | 0.5473 | 0.3991 | 0.4822 | 0.2799 | 1.1540 | 0.5819 | 0.9045 | 0.2990 | 12.774 | 0.7117 | 7.0169 | 3.7457 | 0.8 | 0.3621 | 0.2961 | 0.3443 | 0.2425 | 0.5473 | 0.3845 | 0.5031 | 0.2718 | 1.1540 | 0.5454 | 0.9830 | 0.2910 | 12.774 | 0.6314 | 8.7375 | 4.9990 | 0.9 | 0.3621 | 0.29 | 0.353 | 0.2385 | 0.5473 | 0.3718 | 0.5248 | 0.2646 | 1.1540 | 0.5139 | 1.0661 | 0.2876 | 12.774 | 0.5708 | 10.656 | 6.4505 | 1.0 | 0.3621 | 0.2844 | 0.3621 | 0.2348 | 0.5473 | 0.3601 | 0.5473 | 0.2583 | 1.1540 | 0.4867 | 1.1540 | 0.2890 | 12.774 | 0.5239 | 12.774 | 8.1003 |
| 5 | 0.1 | 8.0209 | 7.7585 | 6.1372 | 5.7600 | 12.967 | 12.232 | 8.3642 | 7.5029 | 28.462 | 24.840 | 12.067 | 9.5146 | 319.35 | 102.39 | 17.451 | 4.1230 | 0.2 | 8.0209 | 7.5109 | 6.3314 | 5.5771 | 12.967 | 11.567 | 8.8169 | 7.0943 | 28.462 | 21.945 | 13.492 | 8.3869 | 319.35 | 56.008 | 31.445 | 4.7897 | 0.3 | 8.0209 | 7.2770 | 6.5294 | 5.3980 | 12.967 | 10.962 | 9.2843 | 6.7003 | 28.462 | 19.588 | 15.017 | 7.3584 | 319.35 | 36.978 | 50.327 | 10.344 | 0.4 | 8.0209 | 7.0557 | 6.7311 | 5.2226 | 12.967 | 10.411 | 9.7664 | 6.321 | 28.462 | 17.641 | 16.640 | 6.4290 | 319.35 | 26.816 | 74.095 | 20.784 | 0.5 | 8.0209 | 6.8461 | 6.9367 | 5.0510 | 12.967 | 9.9071 | 10.263 | 5.9564 | 28.462 | 16.010 | 18.362 | 5.5988 | 319.35 | 20.580 | 102.75 | 36.112 | 0.6 | 8.0209 | 6.6474 | 7.146 | 4.8832 | 12.967 | 9.4445 | 10.775 | 5.6065 | 28.462 | 14.627 | 20.184 | 4.8677 | 319.35 | 16.415 | 136.29 | 56.327 | 0.7 | 8.0209 | 6.4588 | 7.3591 | 4.7192 | 12.967 | 9.0189 | 11.301 | 5.2713 | 28.462 | 13.442 | 22.105 | 4.2357 | 319.35 | 13.467 | 174.72 | 81.429 | 0.8 | 8.0209 | 6.2795 | 7.5759 | 4.5589 | 12.967 | 8.6262 | 11.842 | 4.9508 | 28.462 | 12.418 | 24.124 | 3.7028 | 319.35 | 11.293 | 218.04 | 111.42 | 0.9 | 8.0209 | 6.1090 | 7.7953 | 4.4024 | 12.967 | 8.2630 | 12.397 | 4.6450 | 28.462 | 11.526 | 26.243 | 3.2691 | 319.35 | 9.6369 | 266.24 | 146.30 | 1.0 | 8.0209 | 5.9467 | 8.0209 | 4.2497 | 12.967 | 7.9262 | 12.967 | 4.3538 | 28.462 | 10.741 | 28.462 | 2.9345 | 319.35 | 8.3433 | 319.33 | 186.06 |
| 10 | 0.1 | 31.993 | 30.939 | 24.421 | 22.901 | 51.819 | 48.871 | 33.333 | 29.865 | 113.84 | 99.331 | 48.088 | 37.822 | 1277.4 | 409.25 | 69.149 | 15.713 | 0.2 | 31.993 | 29.945 | 25.203 | 22.163 | 51.819 | 46.201 | 35.155 | 28.218 | 113.84 | 87.726 | 53.814 | 33.282 | 1277.4 | 223.57 | 125.20 | 18.323 | 0.3 | 31.993 | 29.005 | 26.000 | 21.440 | 51.819 | 43.775 | 37.034 | 26.629 | 113.84 | 78.278 | 59.935 | 29.137 | 1277.4 | 147.37 | 200.79 | 40.484 | 0.4 | 31.993 | 28.116 | 26.812 | 20.731 | 51.819 | 41.561 | 38.972 | 25.098 | 113.84 | 70.466 | 66.450 | 25.387 | 1277.4 | 106.67 | 295.94 | 82.197 | 0.5 | 31.993 | 27.274 | 27.639 | 20.038 | 51.819 | 39.536 | 40.968 | 23.626 | 113.84 | 63.919 | 73.361 | 22.031 | 1277.4 | 81.687 | 410.64 | 143.46 | 0.6 | 31.993 | 26.474 | 28.480 | 19.359 | 51.819 | 37.677 | 43.022 | 22.211 | 113.84 | 58.368 | 80.667 | 19.071 | 1277.4 | 64.998 | 544.90 | 224.28 | 0.7 | 31.993 | 25.715 | 29.336 | 18.695 | 51.819 | 35.966 | 45.134 | 20.855 | 113.84 | 53.612 | 88.368 | 16.506 | 1277.4 | 53.189 | 698.70 | 324.65 | 0.8 | 31.993 | 24.994 | 30.207 | 18.045 | 51.819 | 34.387 | 47.304 | 19.557 | 113.84 | 49.498 | 96.464 | 14.336 | 1277.4 | 44.476 | 872.06 | 444.57 | 0.9 | 31.993 | 24.307 | 31.092 | 17.411 | 51.819 | 32.926 | 49.533 | 18.316 | 113.84 | 45.910 | 104.96 | 12.562 | 1277.4 | 37.839 | 1065.0 | 584.04 | 1.0 | 31.993 | 23.654 | 31.993 | 16.791 | 51.819 | 31.570 | 51.819 | 17.134 | 113.84 | 42.758 | 113.84 | 11.182 | 1277.4 | 32.655 | 1277.4 | 743.07 |
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