Research Article
Some New Robust Estimators for Circular Logistic Regression Model with Applications on Meteorological and Ecological Data
Table 6
Bias and
of all methods for data with various percentages of bad leverage points (5%, 10%, and 20%).
| | % of misc error | Methods | | | | Bias | | Bias | | Bias | |
| 1 | 5 | | 1.4570 | 2.1918 | 1.3461 | 2.2028 | 1.2350 | 2.1017 | | 0.1400 | 0.3073 | 0.2511 | 0.4184 | 0.2410 | 0.4293 | | 0.5148 | 0.4482 | 0.6259 | 0.5593 | 0.5159 | 0.4472 | | 0.1344 | 0.3765 | 0.1455 | 0.3654 | 0.1344 | 0.3543 | | 0.1745 | 0.3842 | 0.1634 | 0.3732 | 0.1523 | 0.3621 | 2 | | 1.6681 | 2.3829 | 1.5572 | 2.4139 | 1.4461 | 2.3128 | | 0.3511 | 0.5184 | 0.4622 | 0.6295 | 0.4521 | 0.6384 | | 0.7259 | 0.6593 | 0.8368 | 0.7684 | 0.7268 | 0.6583 | | 0.3455 | 0.5874 | 0.3666 | 0.5765 | 0.3455 | 0.5654 | | 0.3856 | 0.5953 | 0.3745 | 0.5843 | 0.3634 | 0.4732 | 6 | | 1.5571 | 2.2719 | 1.4462 | 2.3029 | 1.3351 | 2.2018 | | 0.2401 | 0.4074 | 0.3512 | 0.5185 | 0.3411 | 0.5274 | | 0.6149 | 0.5483 | 0.7258 | 0.6574 | 0.6158 | 0.5473 | | 0.2345 | 0.4764 | 0.2556 | 0.4655 | 0.2345 | 0.4544 | | 0.2746 | 0.4843 | 0.2635 | 0.4733 | 0.2524 | 0.3622 | 10 | | 1.5560 | 2.2708 | 1.4451 | 2.3018 | 1.3340 | 2.2007 | | 0.2400 | 0.4063 | 0.3501 | 0.5174 | 0.3400 | 0.5263 | | 0.6138 | 0.5472 | 0.7247 | 0.6563 | 0.6147 | 0.5462 | | 0.2334 | 0.4753 | 0.2545 | 0.4644 | 0.2334 | 0.4533 | | 0.2735 | 0.4832 | 0.2624 | 0.4722 | 0.2513 | 0.3611 | 15 | | 1.4450 | 2.1607 | 1.3341 | 2.2007 | 1.2230 | 2.1106 | | 0.1310 | 0.3052 | 0.2400 | 0.4063 | 0.2310 | 0.4152 | | 0.5027 | 0.5361 | 0.6136 | 0.5452 | 0.5036 | 0.4351 | | 0.1233 | 0.3643 | 0.1434 | 0.3533 | 0.1223 | 0.3422 | | 0.1624 | 0.3721 | 0.1513 | 0.3611 | 0.1402 | 0.2500 | 1 | 10 | | 2.4648 | 6.1013 | 2.3538 | 6.0903 | 2.2428 | 6.1813 | | 0.3484 | 0.2098 | 0.2374 | 0.1988 | 0.2374 | 0.1988 | | 1.1933 | 1.4598 | 1.0822 | 1.3487 | 1.0711 | 1.2376 | | 0.2542 | 0.1716 | 0.1431 | 0.0605 | 0.0320 | 0.1514 | | 0.0565 | 0.1120 | 0.1454 | 0.0010 | 0.0343 | 0.0120 | 2 | | 2.4846 | 6.1310 | 2.3835 | 6.0309 | 2.2824 | 6.1318 | | 0.4584 | 0.2098 | 0.3474 | 0.2888 | 0.3474 | 0.2888 | | 1.2833 | 1.5698 | 1.1722 | 1.4587 | 1.1811 | 1.3476 | | 0.3642 | 0.2816 | 0.2531 | 0.1705 | 0.1420 | 0.2614 | | 0.0675 | 0.1230 | 0.1564 | 0.0120 | 0.0453 | 0.0220 | 6 | | 2.4956 | 6.1420 | 2.3945 | 6.0419 | 2.2934 | 6.1428 | | 0.4694 | 0.2188 | 0.3584 | 0.2998 | 0.3584 | 0.2998 | | 1.2943 | 1.5788 | 1.1832 | 1.4697 | 1.1921 | 1.3586 | | 0.3752 | 0.2926 | 0.2641 | 0.1815 | 0.1530 | 0.2724 | | 0.0785 | 0.1340 | 0.1674 | 0.0230 | 0.0563 | 0.0320 | 10 | | 1.5866 | 5.0310 | 1.4035 | 5.2529 | 2.1824 | 6.2538 | | 0.3505 | 0.1099 | 0.4695 | 0.1809 | 0.4673 | 0.3009 | | 1.3053 | 1.6898 | 1.2942 | 1.5707 | 1.2031 | 1.3586 | | 0.4862 | 0.3036 | 0.3751 | 0.2925 | 0.2640 | 0.3834 | | 0.0896 | 0.1451 | 0.1785 | 0.0341 | 0.0674 | 0.0431 | 15 | | 1.6977 | 5.1421 | 1.5146 | 5.3630 | 2.2935 | 6.3549 | | 0.4616 | 0.2188 | 0.5706 | 0.2918 | 0.5784 | 0.4108 | | 1.4164 | 1.7999 | 1.3953 | 1.6818 | 1.3142 | 1.4697 | | 0.5973 | 0.4147 | 0.4861 | 0.3836 | 0.3751 | 0.4945 | | 0.1985 | 0.1662 | 0.1996 | 0.0552 | 0.0874 | 0.0541 | 1 | 20 | | 2.7288 | 7.4773 | 2.9308 | 7.6983 | 2.0918 | 7.7093 | | 0.4309 | 0.6467 | 0.5410 | 0.7578 | 0.5521 | 0.7689 | | 1.6603 | 2.8031 | 1.5512 | 2.7120 | 0.7623 | 1.9231 | | 0.7688 | 1.3257 | 0.8876 | 1.5732 | 0.6987 | 0.4621 | | 0.0703 | 0.3217 | 0.0814 | 0.3328 | 0.0925 | 0.3439 | 2 | | 2.6178 | 7.3663 | 2.8218 | 7.5873 | 2.1808 | 7.6183 | | 0.3219 | 0.5357 | 0.4300 | 0.6468 | 0.4411 | 0.6579 | | 1.5413 | 2.7121 | 1.4322 | 2.6010 | 0.6513 | 1.8121 | | 0.6578 | 1.2147 | 0.7766 | 1.4622 | 0.5877 | 0.3511 | | 0.0612 | 0.3106 | 0.0703 | 0.3217 | 0.0814 | 0.3328 | 6 | | 2.7288 | 7.4773 | 2.9328 | 7.6983 | 2.2918 | 7.7293 | | 0.4329 | 0.6467 | 0.5410 | 0.7578 | 0.5521 | 0.7689 | | 1.6523 | 2.8231 | 1.5432 | 2.7120 | 0.7623 | 1.9231 | | 0.7688 | 1.3257 | 0.8876 | 1.5732 | 0.6987 | 0.4621 | | 0.0723 | 0.3217 | 0.0812 | 0.3106 | 0.0703 | 0.3217 | 10 | | 2.7288 | 7.4773 | 2.9328 | 7.6983 | 2.2918 | 7.7293 | | 0.4329 | 0.6467 | 0.5410 | 0.7578 | 0.5521 | 0.7689 | | 1.6523 | 2.8231 | 1.5432 | 2.7120 | 0.7623 | 1.9231 | | 0.7688 | 1.3257 | 0.8876 | 1.5732 | 0.6987 | 0.4621 | | 0.0723 | 0.3217 | 0.0812 | 0.3106 | 0.0703 | 0.3217 | 15 | | 3.6178 | 6.3663 | 1.8418 | 6.5873 | 1.1808 | 6.6183 | | 0.5439 | 0.7567 | 0.6520 | 0.8678 | 0.6631 | 0.8789 | | 2.5412 | 1.7120 | 0.7543 | 1.8231 | 1.8534 | 2.8120 | | 1.6577 | 1.6368 | 1.7985 | 2.4843 | 1.5876 | 0.6510 | | 0.1612 | 0.4106 | 0.1701 | 0.4105 | 0.1612 | 0.4106 |
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