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 6 五个总体时六种Bootstrap置信区间的模拟区间长度

(λ1, λ2, λ3, λ4, λ5) = (3, 3, 4, 4, 5) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1557 0.1978 0.1363 3.4939 4.6909 3.2412 0.1216 0.1617 0.1078 2.8773 3.4579 2.3837 $\eta _{2}^{2}$ 0.2734 0.3518 0.2424 8.2839 11.5465 7.9518 0.2131 0.2876 0.1917 6.2643 8.7179 5.9407 $\eta _{3}^{2}$ 0.4387 0.5513 0.3804 17.0336 22.4545 15.4017 0.3928 0.4504 0.3005 13.6951 17.0843 11.6810 $\eta _{4}^{2}$ 1.0438 1.0821 0.7472 29.4770 38.7087 26.8397 0.7844 0.8838 0.5901 25.7350 29.3646 20.3567 $\eta _{5}^{2}$ 1.4713 1.7906 1.2372 44.0148 60.0451 41.9806 1.2714 1.4625 0.9766 37.1142 45.4880 31.8257 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1027 0.1398 0.0902 2.5296 2.8396 1.9479 0.0935 0.1159 0.0733 1.8318 2.4289 1.6117 $\eta _{2}^{2}$ 0.2213 0.2485 0.1604 5.2675 7.0858 4.7783 0.1706 0.2060 0.1304 4.2271 5.9759 3.9423 $\eta _{3}^{2}$ 0.3330 0.3895 0.2515 10.8420 13.8792 9.3431 0.2479 0.3226 0.2044 9.5049 11.5423 7.6441 $\eta _{4}^{2}$ 0.5100 0.7648 0.4939 21.4102 24.0453 16.3943 0.5928 0.6331 0.4013 17.7956 20.1387 13.4950 $\eta _{5}^{2}$ 0.9985 1.2659 0.8175 26.7238 37.3193 25.6653 0.8089 1.0476 0.6642 22.7187 31.3854 21.2205 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0822 0.1093 0.0687 1.7325 2.0830 1.3409 0.0628 0.0822 0.0494 1.6502 1.6998 1.0693 $\eta _{2}^{2}$ 0.1728 0.1943 0.1221 3.6881 5.0325 3.3183 0.1143 0.1462 0.0879 3.3868 4.1695 2.6306 $\eta _{3}^{2}$ 0.2729 0.3044 0.1915 8.6829 9.8244 6.4719 0.1815 0.2290 0.1378 8.1659 8.2079 5.2124 $\eta _{4}^{2}$ 0.5130 0.5974 0.3761 16.8130 17.2494 11.4077 0.4510 0.4493 0.2705 14.5028 14.2889 9.0520 $\eta _{5}^{2}$ 0.7733 0.9888 0.6224 24.5885 26.9702 17.9168 0.5895 0.7434 0.4476 16.8295 22.2257 14.1171 (λ1, λ2, λ3, λ4, λ5) = (4, 4, 5, 5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1462 0.1915 0.1272 3.2911 4.4496 3.0456 0.1088 0.1479 0.0948 2.7034 3.2557 2.2115 $\eta _{2}^{2}$ 0.2565 0.3406 0.2263 7.8440 11.0346 7.5213 0.1904 0.2630 0.1686 5.8552 8.2163 5.5371 $\eta _{3}^{2}$ 0.4124 0.5337 0.3552 16.2008 21.4728 14.5817 0.3571 0.4118 0.2644 12.8877 16.0774 10.8849 $\eta _{4}^{2}$ 0.9921 1.0475 0.6977 27.9733 36.9794 25.3735 0.7145 0.8081 0.5192 24.2983 27.6426 18.9434 $\eta _{5}^{2}$ 1.3857 1.7332 1.1552 41.6062 57.3327 39.6393 1.1556 1.3371 0.8594 34.8158 42.8044 29.5654 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0880 0.1214 0.0758 2.3754 2.6513 1.7957 0.0791 0.0964 0.0591 1.7105 2.2721 1.4887 $\eta _{2}^{2}$ 0.1951 0.2159 0.1348 4.9387 6.6647 4.4483 0.1449 0.1714 0.1051 3.9676 5.6446 3.6908 $\eta _{3}^{2}$ 0.2919 0.3383 0.2114 10.1844 13.0444 8.6890 0.2077 0.2684 0.1648 8.9952 10.9070 7.1541 $\eta _{4}^{2}$ 0.4294 0.6643 0.4151 20.2033 22.5874 15.1945 0.5139 0.5266 0.3234 16.8518 19.0010 12.5837 $\eta _{5}^{2}$ 0.8652 1.0995 0.6871 24.7762 35.0130 23.7310 0.6784 0.8714 0.5352 21.1760 29.5517 19.7318 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0696 0.0912 0.0561 1.6539 1.9649 1.2599 0.0532 0.0672 0.0400 1.6002 1.6103 1.0197 $\eta _{2}^{2}$ 0.1504 0.1622 0.0998 3.5044 4.7685 3.1352 0.0973 0.1195 0.0712 3.2736 3.9771 2.5161 $\eta _{3}^{2}$ 0.2378 0.2540 0.1565 8.3027 9.2860 6.0901 0.1548 0.1872 0.1116 7.9416 7.8271 4.9874 $\eta _{4}^{2}$ 0.4440 0.4984 0.3073 16.1106 16.2937 10.7029 0.3986 0.3673 0.2191 14.0896 13.6050 8.6378 $\eta _{5}^{2}$ 0.6591 0.8249 0.5084 23.4391 25.4566 16.7651 0.5028 0.6077 0.3626 16.1526 21.1227 13.4314 (λ1, λ2, λ3, λ4, λ5) = (7, 7, 8, 8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.1355 0.1836 0.1170 3.0581 4.1632 2.8178 0.0949 0.1315 0.0811 2.5129 3.0279 2.0208 $\eta _{2}^{2}$ 0.2374 0.3266 0.2081 7.3303 10.4187 7.0135 0.1657 0.2338 0.1442 5.4125 7.6619 5.1002 $\eta _{3}^{2}$ 0.3824 0.5116 0.3267 15.2237 20.2877 13.6218 0.3185 0.3661 0.2264 11.9978 14.9555 10.0096 $\eta _{4}^{2}$ 0.9334 1.0040 0.6417 26.2275 34.9196 23.6569 0.6387 0.7184 0.4446 22.7218 25.7450 17.3886 $\eta _{5}^{2}$ 1.2886 1.6610 1.0626 38.8013 54.0965 36.9026 1.0302 1.1885 0.7359 32.3204 39.8907 27.1060 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0747 0.1028 0.0627 2.2214 2.4616 1.6481 0.0685 0.0801 0.0486 1.5998 2.1215 1.3816 $\eta _{2}^{2}$ 0.1715 0.1827 0.1114 4.6076 6.2369 4.1287 0.1260 0.1424 0.0865 3.7212 5.3159 3.4558 $\eta _{3}^{2}$ 0.2548 0.2864 0.1748 9.5321 12.1893 8.0624 0.1780 0.2230 0.1356 8.5029 10.2646 6.6820 $\eta _{4}^{2}$ 0.3566 0.5624 0.3432 18.9937 21.1033 14.0387 0.4556 0.4376 0.2662 15.9378 17.8566 11.7123 $\eta _{5}^{2}$ 0.7446 0.9308 0.5684 22.8372 32.6800 21.8718 0.5819 0.7240 0.4405 19.6857 27.7385 18.3212 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0593 0.0757 0.0464 1.5813 1.8492 1.1884 0.0476 0.0571 0.0347 1.5523 1.5169 0.9747 $\eta _{2}^{2}$ 0.1321 0.1346 0.0825 3.3250 4.5016 2.9623 0.0873 0.1015 0.0617 3.1667 3.7736 2.4147 $\eta _{3}^{2}$ 0.2092 0.2109 0.1294 7.9352 8.7334 5.7341 0.1391 0.1589 0.0967 7.7241 7.4248 4.7839 $\eta _{4}^{2}$ 0.3879 0.4137 0.2540 15.4452 15.3345 10.0587 0.3678 0.3118 0.1899 13.7053 12.8871 8.2708 $\eta _{5}^{2}$ 0.5663 0.6848 0.4202 22.3662 23.9540 15.7304 0.4518 0.5158 0.3143 15.5373 19.9767 12.8403