Table 3 Estimated MSE for different estimators at p = 3 and \(\phi =4\).
\(\rho ^2\) | n | PIGMLE | PIGRRE | PIGGRE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
MLE | \(\hat{k}_1\) | \(\hat{k}_2\) | \(\hat{k}_3\) | \(\hat{k}_4\) | \(\hat{k}_5\) | \(\hat{K}_1\) | \(\hat{K}_2\) | \(\hat{K}_3\) | \(\hat{K}_4\) | \(\hat{K}_5\) | ||
0.80 | 30 | 2.15564 | 1.62867 | 1.26034 | 1.48080 | 1.13092 | 0.91920 | 0.73896 | 0.56563 | 0.42561 | 0.95081 | 0.65980 |
75 | 0.62399 | 0.44114 | 0.33711 | 0.40462 | 0.30984 | 0.25322 | 0.19872 | 0.14992 | 0.13231 | 0.20734 | 0.16961 | |
150 | 0.28150 | 0.24072 | 0.21508 | 0.22843 | 0.17555 | 0.14915 | 0.12432 | 0.10156 | 0.09059 | 0.12330 | 0.11225 | |
200 | 0.21743 | 0.18767 | 0.16806 | 0.17591 | 0.13249 | 0.11321 | 0.09564 | 0.08547 | 0.08455 | 0.09314 | 0.08920 | |
300 | 0.14747 | 0.13257 | 0.12124 | 0.12518 | 0.09427 | 0.08075 | 0.06923 | 0.06381 | 0.06458 | 0.06681 | 0.06582 | |
400 | 0.10194 | 0.09507 | 0.08956 | 0.09106 | 0.07080 | 0.06225 | 0.05492 | 0.05249 | 0.05386 | 0.05418 | 0.05326 | |
0.85 | 30 | 2.12999 | 1.59841 | 1.21674 | 1.42659 | 1.03492 | 0.82703 | 0.64929 | 0.47434 | 0.35167 | 0.82755 | 0.56511 |
75 | 0.85339 | 0.66763 | 0.54621 | 0.62403 | 0.47125 | 0.38334 | 0.30635 | 0.23052 | 0.17563 | 0.35370 | 0.27082 | |
150 | 0.32325 | 0.25889 | 0.21966 | 0.24128 | 0.17382 | 0.14389 | 0.11674 | 0.09707 | 0.09097 | 0.11582 | 0.10499 | |
200 | 0.28602 | 0.24337 | 0.21510 | 0.23000 | 0.17163 | 0.14315 | 0.11746 | 0.09388 | 0.07967 | 0.11609 | 0.10566 | |
300 | 0.15523 | 0.14109 | 0.12985 | 0.13407 | 0.09973 | 0.08410 | 0.06993 | 0.05734 | 0.05135 | 0.06550 | 0.06350 | |
400 | 0.12983 | 0.11635 | 0.10633 | 0.10981 | 0.08100 | 0.06861 | 0.05759 | 0.04984 | 0.04786 | 0.05331 | 0.05320 | |
0.90 | 30 | 5.95678 | 4.45542 | 3.31046 | 3.62954 | 1.85292 | 1.38258 | 1.05263 | 0.76455 | 0.52849 | 1.65059 | 0.92996 |
75 | 1.49481 | 1.13027 | 0.88044 | 1.06255 | 0.77398 | 0.60630 | 0.47192 | 0.34292 | 0.23640 | 0.59671 | 0.41647 | |
150 | 0.46122 | 0.32829 | 0.25511 | 0.30053 | 0.21332 | 0.17059 | 0.13194 | 0.09783 | 0.08358 | 0.13285 | 0.11247 | |
200 | 0.35818 | 0.29545 | 0.25558 | 0.27933 | 0.20138 | 0.16281 | 0.12847 | 0.09377 | 0.07187 | 0.12901 | 0.11151 | |
300 | 0.21791 | 0.19108 | 0.17142 | 0.18057 | 0.13106 | 0.10847 | 0.08775 | 0.06745 | 0.05537 | 0.08265 | 0.07756 | |
400 | 0.17353 | 0.14721 | 0.12981 | 0.13643 | 0.09369 | 0.07638 | 0.06094 | 0.04827 | 0.04352 | 0.05559 | 0.05384 | |
0.95 | 30 | 5.85553 | 4.23101 | 3.06481 | 3.50715 | 2.05555 | 1.53282 | 1.14824 | 0.82090 | 0.57591 | 1.78159 | 0.99895 |
75 | 1.89321 | 1.20766 | 0.77528 | 1.00843 | 0.60700 | 0.43625 | 0.30484 | 0.19204 | 0.13538 | 0.40659 | 0.24463 | |
150 | 0.88355 | 0.61185 | 0.44801 | 0.55063 | 0.36559 | 0.27905 | 0.20833 | 0.14320 | 0.10411 | 0.24542 | 0.17560 | |
200 | 0.84905 | 0.62570 | 0.48226 | 0.58130 | 0.38819 | 0.29221 | 0.21706 | 0.14866 | 0.10070 | 0.24856 | 0.18581 | |
300 | 0.51988 | 0.40558 | 0.32990 | 0.38636 | 0.26687 | 0.20256 | 0.15180 | 0.10410 | 0.06906 | 0.16151 | 0.13076 | |
400 | 0.28943 | 0.23742 | 0.20348 | 0.22272 | 0.15762 | 0.12396 | 0.09570 | 0.06783 | 0.04804 | 0.09500 | 0.08289 | |
0.99 | 30 | 45.55769 | 29.48378 | 18.00619 | 19.99563 | 4.23131 | 2.63187 | 1.70194 | 1.02752 | 0.62923 | 4.79892 | 1.37238 |
75 | 10.41812 | 6.79721 | 4.30754 | 4.97318 | 1.47997 | 0.91597 | 0.55986 | 0.29412 | 0.17674 | 1.19741 | 0.41395 | |
150 | 4.93233 | 3.78519 | 2.89201 | 3.38328 | 1.67366 | 1.10657 | 0.75795 | 0.48877 | 0.26770 | 1.35780 | 0.65364 | |
200 | 3.45022 | 2.33896 | 1.54919 | 1.90179 | 0.83609 | 0.51968 | 0.32810 | 0.18562 | 0.10020 | 0.53587 | 0.26210 | |
300 | 2.48682 | 1.48487 | 0.83898 | 1.09458 | 0.44296 | 0.27583 | 0.16921 | 0.08911 | 0.05474 | 0.23260 | 0.12536 | |
400 | 1.68915 | 1.09843 | 0.70556 | 0.92756 | 0.44143 | 0.28157 | 0.17855 | 0.09780 | 0.05495 | 0.23097 | 0.13824 |