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 4 两个总体时六种Bootstrap置信区间的模拟区间长度

(λ1, λ2) = (3, 4) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0411 0.0221 0.0154 1.2987 1.0654 0.6986 0.0275 0.0201 0.0137 1.0710 0.9018 0.5738 $\eta _{2}^{2}$ 0.1802 0.1991 0.1384 4.9169 6.6592 4.3665 0.1553 0.1808 0.1236 4.1442 5.6363 3.5863 $\eta _{3}^{2}$ 0.4284 0.5529 0.3845 13.9794 17.0478 11.1784 0.4068 0.5022 0.3360 10.8372 14.4292 9.1810 $\eta _{4}^{2}$ 0.8817 1.0838 0.7537 36.8349 52.2064 34.2320 0.8903 0.9845 0.6729 32.5810 44.1873 28.1151 $\eta _{5}^{2}$ 1.3595 1.7916 1.2460 74.1995 106.5424 69.8603 1.4416 1.6275 1.1124 61.4367 90.1772 57.3771 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0252 0.0171 0.0112 0.8519 0.7178 0.4647 0.0383 0.0129 0.0083 0.5550 0.5160 0.3071 $\eta _{2}^{2}$ 0.1485 0.1539 0.1009 3.2747 4.4861 2.9044 0.1147 0.1164 0.0746 2.5189 3.2254 1.9195 $\eta _{3}^{2}$ 0.3626 0.4274 0.2802 9.6313 11.4847 7.4355 0.2774 0.3235 0.2072 6.4404 8.2571 4.9140 $\eta _{4}^{2}$ 0.5683 0.8377 0.5493 26.9447 35.1702 22.7699 0.5835 0.6340 0.4062 21.0352 25.2859 15.0482 $\eta _{5}^{2}$ 1.2108 1.3848 0.9080 48.5261 71.7750 46.4686 0.8832 1.0481 0.6715 32.1665 51.6033 30.7102 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0336 0.0110 0.0068 0.6014 0.3940 0.2379 0.0345 0.0092 0.0056 0.4908 0.3422 0.2053 $\eta _{2}^{2}$ 0.0935 0.0986 0.0615 1.8589 2.4626 1.4867 0.1076 0.0826 0.0503 1.7424 2.1391 1.2834 $\eta _{3}^{2}$ 0.2080 0.2740 0.1708 5.7627 6.3043 3.8061 0.2012 0.2295 0.1397 5.5726 5.4763 3.2856 $\eta _{4}^{2}$ 0.4737 0.5371 0.3349 13.8291 19.3065 11.6555 0.3902 0.4499 0.2739 13.5280 16.7701 10.0614 $\eta _{5}^{2}$ 0.8088 0.8878 0.5536 27.4740 39.4007 23.7863 0.6367 0.7437 0.4527 21.7438 34.2241 20.5332 (λ1, λ2) = (5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0394 0.0210 0.0138 1.2360 1.0023 0.6375 0.0255 0.0183 0.0118 0.9932 0.8023 0.5009 $\eta _{2}^{2}$ 0.1646 0.1887 0.1243 4.5252 6.2645 3.9848 0.1372 0.1645 0.1064 3.6578 5.0143 3.1310 $\eta _{3}^{2}$ 0.3848 0.5242 0.3452 12.9767 16.0372 10.2012 0.3566 0.4568 0.2956 9.5920 12.8368 8.0154 $\eta _{4}^{2}$ 0.7964 1.0275 0.6766 33.7643 49.1118 31.2397 0.7917 0.8955 0.5795 28.7679 39.3111 24.5460 $\eta _{5}^{2}$ 1.2185 1.6985 1.1185 67.9331 100.2271 63.7537 1.2786 1.4804 0.9579 53.6549 80.2260 50.0932 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0228 0.0143 0.0089 0.7857 0.6215 0.3957 0.0361 0.0098 0.0061 0.5066 0.4393 0.2632 $\eta _{2}^{2}$ 0.1275 0.1287 0.0803 2.8605 3.8848 2.4733 0.0952 0.0879 0.0545 2.2166 2.7457 1.6448 $\eta _{3}^{2}$ 0.3042 0.3575 0.2231 8.5709 9.9451 6.3316 0.2233 0.2441 0.1515 5.6665 7.0291 4.2107 $\eta _{4}^{2}$ 0.4537 0.7008 0.4373 23.6974 30.4554 19.3897 0.4774 0.4785 0.2969 18.6652 21.5255 12.8946 $\eta _{5}^{2}$ 1.0214 1.1585 0.7229 41.8990 62.1532 39.5704 0.7079 0.7911 0.4908 27.3300 43.9289 26.3153 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0319 0.0080 0.0049 0.5740 0.3437 0.2114 0.0331 0.0068 0.0042 0.4703 0.3005 0.1874 $\eta _{2}^{2}$ 0.0777 0.0724 0.0444 1.6875 2.1483 1.3215 0.0953 0.0616 0.0375 1.6146 1.8781 1.1713 $\eta _{3}^{2}$ 0.1642 0.2010 0.1233 5.3241 5.4997 3.3830 0.1670 0.1712 0.1042 5.2454 4.8079 2.9985 $\eta _{4}^{2}$ 0.3879 0.3939 0.2416 12.4861 16.8425 10.3598 0.3232 0.3355 0.2043 12.5257 14.7231 9.1822 $\eta _{5}^{2}$ 0.6670 0.6512 0.3994 24.7334 34.3722 21.1422 0.5259 0.5546 0.3377 19.6984 30.0466 18.7387 (λ1, λ2) = (8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0386 0.0204 0.0131 1.2039 0.9676 0.6056 0.0246 0.0174 0.0109 0.9618 0.7591 0.4681 $\eta _{2}^{2}$ 0.1578 0.1837 0.1180 4.3248 6.0474 3.7849 0.1297 0.1563 0.0984 3.4612 4.7443 2.9255 $\eta _{3}^{2}$ 0.3660 0.5103 0.3279 12.4635 15.4815 9.6895 0.3357 0.4342 0.2733 9.0888 12.1456 7.4894 $\eta _{4}^{2}$ 0.7595 1.0002 0.6427 32.1929 47.4100 29.6727 0.7508 0.8511 0.5357 27.2271 37.1946 22.9350 $\eta _{5}^{2}$ 1.1574 1.6535 1.0625 64.7261 96.7542 60.5558 1.2110 1.4069 0.8856 50.5105 75.9066 46.8056 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0219 0.0131 0.0080 0.7570 0.5777 0.3643 0.0355 0.0088 0.0054 0.4892 0.4095 0.2485 $\eta _{2}^{2}$ 0.1190 0.1178 0.0721 2.6816 3.6109 2.2768 0.0897 0.0788 0.0486 2.1073 2.5595 1.5533 $\eta _{3}^{2}$ 0.2806 0.3272 0.2004 8.1129 9.2440 5.8287 0.2080 0.2188 0.1351 5.3869 6.5525 3.9764 $\eta _{4}^{2}$ 0.4076 0.6413 0.3927 22.2950 28.3083 17.8497 0.4473 0.4288 0.2648 17.8090 20.0658 12.1772 $\eta _{5}^{2}$ 0.9453 1.0601 0.6492 39.0370 57.7713 36.4275 0.6581 0.7089 0.4378 25.5826 40.9500 24.8510 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.0314 0.0072 0.0045 0.5646 0.3261 0.2034 0.0329 0.0063 0.0039 0.4632 0.2855 0.1814 $\eta _{2}^{2}$ 0.0738 0.0651 0.0404 1.6289 2.0381 1.2713 0.0928 0.0564 0.0347 1.5702 1.7846 1.1336 $\eta _{3}^{2}$ 0.1535 0.1809 0.1123 5.1740 5.2176 3.2545 0.1599 0.1566 0.0965 5.1318 4.5686 2.9020 $\eta _{4}^{2}$ 0.3669 0.3546 0.2201 12.0263 15.9787 9.9664 0.3092 0.3069 0.1891 12.1779 13.9902 8.8866 $\eta _{5}^{2}$ 0.6322 0.5862 0.3639 23.7951 32.6094 20.3393 0.5028 0.5073 0.3126 18.9885 28.5507 18.1355