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 2 三个总体时六种Bootstrap置信区间的模拟覆盖概率

(λ1, λ2, λ3) = (3, 3, 4) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.8655 0.8396 0.8668 0.9330 0.9144 0.9428 0.9085 0.8744 0.9080 0.9580 0.9388 0.9620 $\eta _{2}^{2}$ 0.8675 0.8380 0.8668 0.9335 0.9180 0.9424 0.9080 0.8724 0.9076 0.9565 0.9432 0.9608 $\eta _{3}^{2}$ 0.8685 0.8348 0.8668 0.9310 0.9216 0.9408 0.9065 0.8708 0.9084 0.9560 0.9480 0.9620 $\eta _{4}^{2}$ 0.8690 0.8340 0.8672 0.9320 0.9248 0.9396 0.9080 0.8708 0.9104 0.9550 0.9492 0.9620 $\eta _{5}^{2}$ 0.8690 0.8336 0.8676 0.9315 0.9228 0.9412 0.9060 0.8712 0.9088 0.9560 0.9484 0.9620 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9230 0.8804 0.9324 0.9580 0.9320 0.9624 0.9400 0.8988 0.9416 0.9615 0.9336 0.9664 $\eta _{2}^{2}$ 0.9205 0.8736 0.9344 0.9570 0.9380 0.9624 0.9415 0.8976 0.9412 0.9605 0.9352 0.9664 $\eta _{3}^{2}$ 0.9275 0.8708 0.9340 0.9560 0.9436 0.9624 0.9420 0.8964 0.9420 0.9605 0.9436 0.9676 $\eta _{4}^{2}$ 0.9295 0.8696 0.9340 0.9545 0.9464 0.9620 0.9445 0.8944 0.9432 0.9590 0.9484 0.9672 $\eta _{5}^{2}$ 0.9275 0.8720 0.9336 0.9560 0.9448 0.9620 0.9435 0.8964 0.9428 0.9605 0.9452 0.9672 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9415 0.8904 0.9448 0.9345 0.9000 0.9456 0.9450 0.8752 0.9420 0.9380 0.8924 0.9448 $\eta _{2}^{2}$ 0.9430 0.8844 0.9452 0.9335 0.9088 0.9448 0.9450 0.8684 0.9420 0.9385 0.9016 0.9452 $\eta _{3}^{2}$ 0.9450 0.8772 0.9448 0.9335 0.9200 0.9456 0.9465 0.8604 0.9424 0.9400 0.9112 0.9452 $\eta _{4}^{2}$ 0.9440 0.8740 0.9448 0.9340 0.9252 0.9452 0.9445 0.8528 0.9424 0.9410 0.9188 0.9448 $\eta _{5}^{2}$ 0.9445 0.8768 0.9440 0.9335 0.9228 0.9452 0.9460 0.8588 0.9424 0.9405 0.9136 0.9448 (λ1, λ2, λ3) = (5, 5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9410 0.9036 0.9444 0.9595 0.9388 0.9664 0.9550 0.9128 0.9588 0.9670 0.9540 0.9756 $\eta _{2}^{2}$ 0.9415 0.9004 0.9440 0.9595 0.9436 0.9664 0.9560 0.9072 0.9596 0.9665 0.9576 0.9756 $\eta _{3}^{2}$ 0.9415 0.8936 0.9448 0.9590 0.9476 0.9656 0.9580 0.9016 0.9608 0.9670 0.9616 0.9752 $\eta _{4}^{2}$ 0.9395 0.8892 0.9452 0.9580 0.9516 0.9644 0.9565 0.8948 0.9616 0.9670 0.9620 0.9744 $\eta _{5}^{2}$ 0.9415 0.8920 0.9444 0.9590 0.9484 0.9652 0.9575 0.9016 0.9612 0.9670 0.9616 0.9752 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9630 0.8964 0.9704 0.9735 0.9432 0.9796 0.9650 0.8976 0.9704 0.9735 0.9444 0.9796 $\eta _{2}^{2}$ 0.9635 0.8852 0.9704 0.9725 0.9492 0.9800 0.9655 0.8904 0.9688 0.9740 0.9516 0.9796 $\eta _{3}^{2}$ 0.9650 0.8672 0.9704 0.9730 0.9576 0.9804 0.9655 0.8760 0.9696 0.9745 0.9588 0.9792 $\eta _{4}^{2}$ 0.9625 0.8608 0.9692 0.9720 0.9620 0.9800 0.9650 0.8660 0.9708 0.9745 0.9628 0.9784 $\eta _{5}^{2}$ 0.9645 0.8652 0.9692 0.9730 0.9604 0.9800 0.9650 0.8744 0.9692 0.9745 0.9604 0.9788 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9665 0.8680 0.9716 0.9520 0.9200 0.9696 0.9595 0.8388 0.9672 0.9595 0.9060 0.9660 $\eta _{2}^{2}$ 0.9650 0.8536 0.9724 0.9510 0.9292 0.9696 0.9595 0.8196 0.9688 0.9585 0.9192 0.9660 $\eta _{3}^{2}$ 0.9650 0.8336 0.9712 0.9515 0.9364 0.9688 0.9620 0.7944 0.9688 0.9585 0.9312 0.9656 $\eta _{4}^{2}$ 0.9660 0.8248 0.9688 0.9520 0.9404 0.9688 0.9625 0.7784 0.9676 0.9585 0.9380 0.9668 $\eta _{5}^{2}$ 0.9655 0.8312 0.9700 0.9520 0.9380 0.9692 0.9620 0.7900 0.9684 0.9585 0.9320 0.9664 (λ1, λ2, λ3) = (6, 8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9510 0.9116 0.9568 0.9650 0.9484 0.9728 0.9625 0.9184 0.9656 0.9765 0.9620 0.9816 $\eta _{2}^{2}$ 0.9510 0.9104 0.9560 0.9650 0.9524 0.9732 0.9620 0.9108 0.9656 0.9755 0.9628 0.9812 $\eta _{3}^{2}$ 0.9525 0.9016 0.9552 0.9650 0.9572 0.9728 0.9640 0.9060 0.9660 0.9735 0.9660 0.9816 $\eta _{4}^{2}$ 0.9510 0.8952 0.9548 0.9655 0.9612 0.9724 0.9640 0.9000 0.9664 0.9730 0.9684 0.9800 $\eta _{5}^{2}$ 0.9530 0.9008 0.9548 0.9650 0.9588 0.9728 0.9645 0.9048 0.9664 0.9730 0.9660 0.9816 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9685 0.8964 0.9748 0.9780 0.9568 0.9820 0.9705 0.9036 0.9744 0.9785 0.9560 0.9828 $\eta _{2}^{2}$ 0.9695 0.8868 0.9756 0.9785 0.9604 0.9824 0.9705 0.8928 0.9740 0.9785 0.9616 0.9824 $\eta _{3}^{2}$ 0.9695 0.8660 0.9756 0.9775 0.9672 0.9820 0.9705 0.8744 0.9744 0.9780 0.9664 0.9824 $\eta _{4}^{2}$ 0.9695 0.8560 0.9760 0.9775 0.9704 0.9820 0.9695 0.8652 0.9756 0.9780 0.9704 0.9824 $\eta _{5}^{2}$ 0.9695 0.8644 0.9756 0.9775 0.9668 0.9820 0.9705 0.8728 0.9740 0.9780 0.9672 0.9828 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9720 0.8676 0.9776 0.9630 0.9324 0.9768 0.9665 0.8388 0.9736 0.9690 0.9224 0.9716 $\eta _{2}^{2}$ 0.9715 0.8516 0.9772 0.9630 0.9372 0.9768 0.9660 0.8068 0.9744 0.9690 0.9320 0.9708 $\eta _{3}^{2}$ 0.9705 0.8300 0.9776 0.9610 0.9468 0.9764 0.9680 0.7800 0.9732 0.9695 0.9428 0.9708 $\eta _{4}^{2}$ 0.9700 0.8156 0.9752 0.9620 0.9520 0.9768 0.9670 0.7604 0.9724 0.9685 0.9492 0.9696 $\eta _{5}^{2}$ 0.9700 0.8272 0.9772 0.9610 0.9476 0.9756 0.9675 0.7748 0.9728 0.9695 0.9452 0.9704