Research Article
A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications
Table 3
Estimated MSE when
n = 100,
, and
ρ = 0.70 and 0.80.
| n = 100 | 0.9 | 0.99 | Sigma | k = d | OLS | Ridge | Liu | New est | OLS | Ridge | Liu | New est |
| 1 | 0.1 | 0.1124 | 0.1121 | 0.1105 | 0.1118 | 0.1492 | 0.1478 | 0.1396 | 0.1465 | | 0.2 | | 0.1118 | 0.1107 | 0.1114 | | 0.1465 | 0.1404 | 0.1441 | | 0.3 | | 0.1116 | 0.1108 | 0.1110 | | 0.1453 | 0.1414 | 0.1420 | | 0.4 | | 0.1114 | 0.1110 | 0.1106 | | 0.1442 | 0.1423 | 0.1401 | | 0.5 | | 0.1112 | 0.1112 | 0.1104 | | 0.1432 | 0.1434 | 0.1384 | | 0.6 | | 0.1110 | 0.1114 | 0.1101 | | 0.1422 | 0.1444 | 0.1369 | | 0.7 | | 0.1108 | 0.1116 | 0.1100 | | 0.1412 | 0.1455 | 0.1356 | | 0.8 | | 0.1106 | 0.1119 | 0.1099 | | 0.1403 | 0.1467 | 0.1345 | | 0.9 | | 0.1105 | 0.1121 | 0.1099 | | 0.1395 | 0.1479 | 0.1336 | | 1 | | 0.1104 | 0.1124 | 0.1099 | | 0.1387 | 0.1492 | 0.1328 |
| 5 | 0.1 | 2.0631 | 2.0452 | 1.9126 | 2.0274 | 3.2440 | 3.1954 | 2.8523 | 3.1472 | | 0.2 | | 2.0276 | 1.9289 | 1.9924 | | 3.1480 | 2.8942 | 3.0538 | | 0.3 | | 2.0102 | 1.9454 | 1.9583 | | 3.1019 | 2.9365 | 2.9638 | | 0.4 | | 1.9932 | 1.9619 | 1.9249 | | 3.0570 | 2.9793 | 2.8771 | | 0.5 | | 1.9764 | 1.9785 | 1.8922 | | 3.0133 | 3.0224 | 2.7934 | | 0.6 | | 1.9599 | 1.9952 | 1.8603 | | 2.9707 | 3.0659 | 2.7128 | | 0.7 | | 1.9436 | 2.0121 | 1.8291 | | 2.9291 | 3.1098 | 2.6350 | | 0.8 | | 1.9276 | 2.0290 | 1.7986 | | 2.8887 | 3.1542 | 2.5600 | | 0.9 | | 1.9119 | 2.0460 | 1.7688 | | 2.8492 | 3.1989 | 2.4876 | | 1 | | 1.8964 | 2.0631 | 1.7396 | | 2.8108 | 3.2440 | 2.4178 |
| 10 | 0.1 | 8.1632 | 8.0901 | 7.5481 | 8.0174 | 12.9200 | 12.7234 | 11.3344 | 12.5287 | | 0.2 | | 8.0182 | 7.6150 | 7.8747 | | 12.5320 | 11.5045 | 12.1511 | | 0.3 | | 7.9474 | 7.6822 | 7.7351 | | 12.3456 | 11.6761 | 11.7867 | | 0.4 | | 7.8777 | 7.7498 | 7.5984 | | 12.1640 | 11.8493 | 11.4349 | | 0.5 | | 7.8091 | 7.8178 | 7.4646 | | 11.9870 | 12.0239 | 11.0953 | | 0.6 | | 7.7415 | 7.8862 | 7.3336 | | 11.8144 | 12.2001 | 10.7674 | | 0.7 | | 7.6750 | 7.9549 | 7.2053 | | 11.6462 | 12.3778 | 10.4506 | | 0.8 | | 7.6096 | 8.0240 | 7.0797 | | 11.4821 | 12.5570 | 10.1447 | | 0.9 | | 7.5451 | 8.0934 | 6.9568 | | 11.3220 | 12.7377 | 9.8490 | | 1 | | 7.4816 | 8.1632 | 6.8364 | | 11.1658 | 12.9200 | 9.5634 |
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