多个偏正态总体共同位置参数的Bootstrap置信区间

叶仁道,王仲池,罗堃,林雅

Bootstrap Confidence Intervals for the Common Location Parameter of Several Skew-Normal Populations

Rendao Ye,Zhongchi Wang,Kun Luo,Ya Lin

表 5 三个总体时六种Bootstrap置信区间的模拟区间长度

(λ1, λ2, λ3) = (3, 3, 4) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1558 0.1979 0.1365 4.3721 6.2373 4.0877 0.1325 0.1794 0.1215 3.7023 5.2625 3.3734 $\eta _{2}^{2}$ 0.3006 0.3512 0.2418 7.7139 11.0764 7.2551 0.2495 0.3182 0.2154 6.4917 9.3478 5.9910 $\eta _{3}^{2}$ 0.4433 0.5465 0.3751 13.3325 17.2881 11.3168 0.4046 0.4949 0.3343 12.2296 14.5935 9.3507 $\eta _{4}^{2}$ 1.0154 1.0665 0.7290 26.7962 33.8652 22.1617 0.7806 0.9649 0.6497 24.4722 28.5907 18.3170 $\eta _{5}^{2}$ 1.5271 1.7688 1.2130 40.0428 56.0040 36.6571 1.3446 1.6015 1.0812 35.8804 47.2769 30.2912 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1100 0.1527 0.0994 3.0012 3.9181 2.4516 0.0906 0.1159 0.0733 2.3937 3.0532 1.8877 $\eta _{2}^{2}$ 0.2372 0.2708 0.1761 4.7556 6.9595 4.3525 0.1882 0.2057 0.1300 3.8212 5.4245 3.3539 $\eta _{3}^{2}$ 0.3379 0.4209 0.2729 9.1752 10.8646 6.7914 0.2753 0.3204 0.2019 6.8204 8.4705 5.2370 $\eta _{4}^{2}$ 0.5451 0.8201 0.5295 16.6665 21.2852 13.3020 0.5376 0.6261 0.3929 12.8209 16.5977 10.2607 $\eta _{5}^{2}$ 1.2405 1.3619 0.8823 25.6048 35.1967 21.9996 0.8750 1.0374 0.6532 19.8941 27.4422 16.9660 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0770 0.0981 0.0608 1.9892 2.3561 1.4262 0.0687 0.0822 0.0494 1.8176 2.0390 1.2296 $\eta _{2}^{2}$ 0.1658 0.1740 0.1077 2.8175 4.1868 2.5327 0.1298 0.1459 0.0875 2.7334 3.6225 2.1837 $\eta _{3}^{2}$ 0.2416 0.2708 0.1668 5.6525 6.5386 3.9525 0.1859 0.2270 0.1356 5.1862 5.6567 3.4092 $\eta _{4}^{2}$ 0.4589 0.5281 0.3235 10.3481 12.8113 7.7421 0.4102 0.4424 0.2631 10.0297 11.0841 6.6801 $\eta _{5}^{2}$ 0.8659 0.8764 0.5392 13.4808 21.1830 12.8039 0.6102 0.7345 0.4385 14.6270 18.3261 11.0449 (λ1, λ2, λ3) = (5, 5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1407 0.1878 0.1222 4.0248 5.8983 3.7440 0.1151 0.1632 0.1041 3.2368 4.6661 2.9283 $\eta _{2}^{2}$ 0.2739 0.3332 0.2165 7.0974 10.4754 6.6448 0.2185 0.2894 0.1845 5.6653 8.2891 5.2006 $\eta _{3}^{2}$ 0.4017 0.5182 0.3357 12.3715 16.3519 10.3646 0.3563 0.4498 0.2864 10.9406 12.9415 8.1174 $\eta _{4}^{2}$ 0.9341 1.0101 0.6519 24.9148 32.0333 20.2967 0.6866 0.8763 0.5565 21.9479 25.3549 15.9014 $\eta _{5}^{2}$ 1.3924 1.6771 1.0854 36.9300 52.9723 33.5725 1.1886 1.4554 0.9262 31.7051 41.9254 26.2962 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0887 0.1279 0.0788 2.6180 3.3553 2.0751 0.0700 0.0875 0.0532 2.1090 2.6020 1.6216 $\eta _{2}^{2}$ 0.1993 0.2269 0.1396 4.0753 5.9608 3.6841 0.1517 0.1552 0.0943 3.3151 4.6228 2.8811 $\eta _{3}^{2}$ 0.2792 0.3524 0.2163 8.1131 9.3072 5.7488 0.2185 0.2419 0.1463 6.0298 7.2186 4.4990 $\eta _{4}^{2}$ 0.4309 0.6860 0.4192 14.5853 18.2361 11.2604 0.4269 0.4728 0.2844 11.2715 14.1454 8.8144 $\eta _{5}^{2}$ 1.0506 1.1400 0.6993 22.1638 30.1523 18.6226 0.6914 0.7832 0.4732 17.3326 23.3868 14.5749 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0593 0.0720 0.0437 1.8513 2.0602 1.2781 0.0558 0.0614 0.0369 1.7059 1.8071 1.1257 $\eta _{2}^{2}$ 0.1345 0.1277 0.0774 2.5730 3.6615 2.2697 0.1069 0.1089 0.0654 2.5355 3.2111 1.9992 $\eta _{3}^{2}$ 0.1932 0.1988 0.1197 5.2713 5.7193 3.5423 0.1503 0.1695 0.1013 4.8778 5.0149 3.1219 $\eta _{4}^{2}$ 0.3651 0.3879 0.2319 9.6019 11.2065 6.9387 0.3410 0.3304 0.1963 9.4261 9.8271 6.1179 $\eta _{5}^{2}$ 0.7096 0.6436 0.3869 12.2461 18.5292 11.4749 0.4951 0.5484 0.3276 13.6283 16.2471 10.1146 (λ1, λ2, λ3) = (6, 8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1374 0.1851 0.1190 3.8328 5.6934 3.5617 0.1115 0.1595 0.1006 3.0461 4.4063 2.7456 $\eta _{2}^{2}$ 0.2679 0.3283 0.2107 6.7565 10.1120 6.3209 0.2122 0.2828 0.1783 5.3267 7.8279 4.8761 $\eta _{3}^{2}$ 0.3922 0.5104 0.3265 11.8395 15.7855 9.8587 0.3464 0.4395 0.2767 10.4123 12.2221 7.6110 $\eta _{4}^{2}$ 0.9154 0.9943 0.6336 23.8733 30.9242 19.3057 0.6669 0.8558 0.5375 20.9130 23.9460 14.9098 $\eta _{5}^{2}$ 1.3617 1.6516 1.0557 35.2072 51.1376 31.9339 1.1564 1.4220 0.8948 29.9936 39.5952 24.6560 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0846 0.1226 0.0748 2.4665 3.1207 1.9302 0.0671 0.0827 0.0503 2.0203 2.4502 1.5399 $\eta _{1}^{2}$ 0.1922 0.2175 0.1324 3.8063 5.5448 3.4270 0.1465 0.1468 0.0890 3.1575 4.3532 2.7361 $\eta _{1}^{2}$ 0.2680 0.3377 0.2051 7.6932 8.6588 5.3476 0.2104 0.2286 0.1381 5.7836 6.7979 4.2725 $\eta _{1}^{2}$ 0.4091 0.6571 0.3973 13.7625 16.9670 10.4745 0.4109 0.4466 0.2685 10.7888 13.3214 8.3705 $\eta _{1}^{2}$ 1.0145 1.0923 0.6630 20.8033 28.0523 17.3230 0.6651 0.7403 0.4467 16.5347 22.0240 13.8411 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0571 0.0680 0.0415 1.8026 1.9617 1.2330 0.0543 0.0586 0.0355 1.6661 1.7271 1.0921 $\eta _{2}^{2}$ 0.1306 0.1207 0.0734 2.4866 3.4866 2.1896 0.1043 0.1040 0.0630 2.4648 3.0692 1.9394 $\eta _{3}^{2}$ 0.1871 0.1879 0.1136 5.1367 5.4466 3.4172 0.1462 0.1618 0.0976 4.7677 4.7936 3.0287 $\eta _{4}^{2}$ 0.3531 0.3666 0.2198 9.3385 10.6722 6.6937 0.3329 0.3155 0.1889 9.2105 9.3939 5.9356 $\eta _{5}^{2}$ 0.6897 0.6083 0.3669 11.8101 17.6458 11.0699 0.4818 0.5237 0.3154 13.2715 15.5304 9.8127