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 3 五个总体时六种Bootstrap置信区间的模拟覆盖概率

(λ1, λ2, λ3, λ4, λ5) = (3, 3, 4, 4, 5) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.8720 0.8332 0.8700 0.9600 0.9280 0.9596 0.9210 0.8760 0.9220 0.9655 0.9220 0.9664 $\eta _{2}^{2}$ 0.8690 0.8368 0.8664 0.9545 0.9144 0.9560 0.9190 0.8836 0.9192 0.9615 0.9148 0.9656 $\eta _{3}^{2}$ 0.8670 0.8412 0.8644 0.9500 0.9088 0.9544 0.9165 0.8868 0.9188 0.9635 0.9112 0.9660 $\eta _{4}^{2}$ 0.8655 0.8440 0.8632 0.9525 0.9196 0.9552 0.9175 0.8900 0.9168 0.9640 0.9228 0.9648 $\eta _{5}^{2}$ 0.8595 0.8504 0.8644 0.9500 0.9280 0.9516 0.9135 0.8948 0.9144 0.9645 0.9224 0.9636 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9300 0.8784 0.9352 0.9630 0.9132 0.9728 0.9405 0.8888 0.9400 0.9535 0.9016 0.9608 $\eta _{2}^{2}$ 0.9290 0.8896 0.9324 0.9650 0.9056 0.9712 0.9390 0.8988 0.9388 0.9545 0.8796 0.9624 $\eta _{3}^{2}$ 0.9270 0.8964 0.9316 0.9655 0.8936 0.9700 0.9395 0.9032 0.9396 0.9625 0.8632 0.9644 $\eta _{4}^{2}$ 0.9260 0.8996 0.9316 0.9635 0.9152 0.9704 0.9390 0.9084 0.9376 0.9615 0.8916 0.9648 $\eta _{5}^{2}$ 0.9240 0.9096 0.9296 0.9640 0.9164 0.9712 0.9380 0.9164 0.9344 0.9615 0.8964 0.9652 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9480 0.8772 0.9444 0.9660 0.9040 0.9672 0.9450 0.8688 0.9380 0.9630 0.8732 0.9640 $\eta _{2}^{2}$ 0.9480 0.8844 0.9440 0.9670 0.8788 0.9700 0.9445 0.8780 0.9376 0.9580 0.8484 0.9620 $\eta _{3}^{2}$ 0.9455 0.8976 0.9420 0.9680 0.8588 0.9692 0.9420 0.8944 0.9376 0.9565 0.8328 0.9572 $\eta _{4}^{2}$ 0.9445 0.9048 0.9416 0.9685 0.8896 0.9692 0.9410 0.9016 0.9364 0.9565 0.8708 0.9580 $\eta _{5}^{2}$ 0.9450 0.9152 0.9412 0.9640 0.8928 0.9684 0.9410 0.9096 0.9364 0.9590 0.8816 0.9588 (λ1, λ2, λ3, λ4, λ5) = (4, 4, 5, 5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9250 0.8764 0.9248 0.9645 0.9248 0.9668 0.9535 0.8948 0.9568 0.9695 0.9172 0.9740 $\eta _{2}^{2}$ 0.9235 0.8808 0.9232 0.9575 0.9096 0.9616 0.9530 0.9016 0.9552 0.9680 0.9088 0.9740 $\eta _{3}^{2}$ 0.9220 0.8900 0.9216 0.9565 0.9012 0.9608 0.9505 0.9124 0.9532 0.9710 0.9036 0.9736 $\eta _{4}^{2}$ 0.9195 0.8940 0.9212 0.9575 0.9144 0.9604 0.9515 0.9168 0.9516 0.9685 0.9164 0.9720 $\eta _{5}^{2}$ 0.9160 0.9016 0.9212 0.9570 0.9188 0.9588 0.9500 0.9252 0.9516 0.9705 0.9188 0.9720 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9540 0.8812 0.9608 0.9675 0.9052 0.9756 0.9555 0.8800 0.9596 0.9620 0.8912 0.9720 $\eta _{2}^{2}$ 0.9545 0.8968 0.9612 0.9700 0.8960 0.9780 0.9565 0.8924 0.9588 0.9580 0.8700 0.9672 $\eta _{3}^{2}$ 0.9525 0.9076 0.9596 0.9710 0.8836 0.9764 0.9545 0.9072 0.9572 0.9645 0.8496 0.9680 $\eta _{4}^{2}$ 0.9490 0.9140 0.9568 0.9700 0.9096 0.9772 0.9530 0.9156 0.9568 0.9640 0.8808 0.9704 $\eta _{5}^{2}$ 0.9450 0.9288 0.9564 0.9705 0.9076 0.9772 0.9530 0.9272 0.9536 0.9650 0.8880 0.9708 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9655 0.8628 0.9640 0.9695 0.8952 0.9692 0.9545 0.8284 0.9536 0.9645 0.8544 0.9684 $\eta _{2}^{2}$ 0.9640 0.8712 0.9632 0.9720 0.8648 0.9736 0.9540 0.8524 0.9532 0.9600 0.8264 0.9624 $\eta _{3}^{2}$ 0.9625 0.8948 0.9632 0.9715 0.8472 0.9748 0.9535 0.8780 0.9516 0.9580 0.8032 0.9584 $\eta _{4}^{2}$ 0.9625 0.9080 0.9620 0.9715 0.8752 0.9748 0.9530 0.8892 0.9528 0.9590 0.8532 0.9596 $\eta _{5}^{2}$ 0.9610 0.9256 0.9608 0.9690 0.8792 0.9744 0.9515 0.9064 0.9504 0.9570 0.8632 0.9608 (λ1, λ2, λ3, λ4, λ5) = (7, 7, 8, 8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9615 0.9072 0.9656 0.9710 0.9228 0.9756 0.9740 0.9080 0.9764 0.9770 0.9176 0.9808 $\eta _{2}^{2}$ 0.9595 0.9152 0.9644 0.9680 0.9060 0.9712 0.9725 0.9172 0.9760 0.9760 0.9100 0.9804 $\eta _{3}^{2}$ 0.9585 0.9236 0.9616 0.9665 0.8972 0.9684 0.9710 0.9308 0.9752 0.9765 0.9048 0.9800 $\eta _{4}^{2}$ 0.9575 0.9308 0.9624 0.9660 0.9120 0.9692 0.9690 0.9400 0.9732 0.9770 0.9156 0.9800 $\eta _{5}^{2}$ 0.9560 0.9372 0.9620 0.9655 0.9132 0.9700 0.9670 0.9516 0.9716 0.9755 0.9168 0.9792 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9750 0.8956 0.9800 0.9755 0.9016 0.9820 0.9735 0.8924 0.9764 0.9675 0.8852 0.9780 $\eta _{2}^{2}$ 0.9735 0.9104 0.9792 0.9765 0.8888 0.9828 0.9735 0.9064 0.9768 0.9670 0.8664 0.9792 $\eta _{3}^{2}$ 0.9705 0.9268 0.9796 0.9750 0.8796 0.9820 0.9725 0.9252 0.9756 0.9725 0.8432 0.9780 $\eta _{4}^{2}$ 0.9695 0.9356 0.9800 0.9745 0.9040 0.9816 0.9715 0.9328 0.9740 0.9725 0.8752 0.9788 $\eta _{5}^{2}$ 0.9670 0.9532 0.9780 0.9750 0.9048 0.9816 0.9695 0.9436 0.9732 0.9725 0.8796 0.9808 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9780 0.8640 0.9800 0.9735 0.8916 0.9748 0.9720 0.8320 0.9764 0.9635 0.8320 0.9732 $\eta _{1}^{2}$ 0.9775 0.8808 0.9800 0.9735 0.8584 0.9768 0.9715 0.8580 0.9756 0.9660 0.8120 0.9696 $\eta _{1}^{2}$ 0.9770 0.9100 0.9792 0.9760 0.8352 0.9800 0.9705 0.8940 0.9748 0.9630 0.7788 0.9680 $\eta _{1}^{2}$ 0.9760 0.9244 0.9792 0.9765 0.8652 0.9812 0.9700 0.9148 0.9736 0.9635 0.8380 0.9692 $\eta _{1}^{2}$ 0.9760 0.9448 0.9776 0.9760 0.8648 0.9800 0.9705 0.9316 0.9728 0.9620 0.8496 0.9692