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 1 两个总体时六种Bootstrap置信区间的模拟覆盖概率

(λ1, λ2) = (3, 4) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.8616 0.8552 0.8740 0.9488 0.9532 0.9460 0.9012 0.8984 0.8980 0.9500 0.9540 0.9548 $\eta _{2}^{2}$ 0.8636 0.8564 0.8748 0.9492 0.9528 0.9464 0.9008 0.8968 0.8980 0.9508 0.9536 0.9548 $\eta _{3}^{2}$ 0.8636 0.8564 0.8752 0.9492 0.9524 0.9472 0.9012 0.8948 0.8988 0.9508 0.9536 0.9548 $\eta _{4}^{2}$ 0.8616 0.8552 0.8740 0.9488 0.9532 0.9460 0.9012 0.8984 0.8980 0.9500 0.9540 0.9548 $\eta _{5}^{2}$ 0.8612 0.8552 0.8736 0.9484 0.9532 0.9460 0.9008 0.9000 0.8980 0.9500 0.9548 0.9536 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9388 0.9224 0.9248 0.9464 0.9544 0.9588 0.9260 0.9324 0.9396 0.9492 0.9544 0.9532 $\eta _{2}^{2}$ 0.9392 0.9196 0.9256 0.9464 0.9536 0.9600 0.9260 0.9292 0.9400 0.9492 0.9532 0.9532 $\eta _{3}^{2}$ 0.9396 0.9196 0.9260 0.9464 0.9536 0.9600 0.9260 0.9284 0.9404 0.9488 0.9528 0.9532 $\eta _{4}^{2}$ 0.9388 0.9224 0.9248 0.9464 0.9544 0.9588 0.9260 0.9324 0.9396 0.9492 0.9544 0.9532 $\eta _{5}^{2}$ 0.9388 0.9224 0.9252 0.9464 0.9548 0.9588 0.9260 0.9332 0.9396 0.9492 0.9544 0.9532 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9236 0.9376 0.9404 0.9412 0.9492 0.9520 0.9284 0.9336 0.9400 0.9472 0.9536 0.9576 $\eta _{2}^{2}$ 0.9240 0.9348 0.9404 0.9408 0.9472 0.9512 0.9288 0.9300 0.9408 0.9468 0.9536 0.9576 $\eta _{3}^{2}$ 0.9244 0.9336 0.9404 0.9408 0.9472 0.9512 0.9288 0.9292 0.9408 0.9472 0.9528 0.9576 $\eta _{4}^{2}$ 0.9236 0.9376 0.9404 0.9412 0.9492 0.9520 0.9284 0.9336 0.9400 0.9472 0.9536 0.9576 $\eta _{5}^{2}$ 0.9228 0.9392 0.9404 0.9412 0.9496 0.9520 0.9284 0.9348 0.9400 0.9472 0.9540 0.9576 (λ1, λ2) = (5, 6) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9312 0.9312 0.9400 0.9652 0.9688 0.9656 0.9548 0.9532 0.9584 0.9656 0.9684 0.9724 $\eta _{2}^{2}$ 0.9320 0.9312 0.9408 0.9652 0.9688 0.9660 0.9556 0.9504 0.9592 0.9656 0.9680 0.9724 $\eta _{3}^{2}$ 0.9328 0.9304 0.9408 0.9652 0.9688 0.9660 0.9556 0.9496 0.9596 0.9656 0.9680 0.9728 $\eta _{4}^{2}$ 0.9312 0.9312 0.9400 0.9652 0.9688 0.9656 0.9548 0.9532 0.9584 0.9656 0.9684 0.9724 $\eta _{5}^{2}$ 0.9312 0.9324 0.9400 0.9652 0.9688 0.9656 0.9548 0.9536 0.9580 0.9660 0.9684 0.9720 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9680 0.9572 0.9660 0.9612 0.9652 0.9724 0.9584 0.9584 0.9680 0.9648 0.9696 0.9716 $\eta _{2}^{2}$ 0.9680 0.9548 0.9660 0.9620 0.9640 0.9724 0.9588 0.9552 0.9680 0.9648 0.9684 0.9716 $\eta _{3}^{2}$ 0.9676 0.9544 0.9664 0.9616 0.9640 0.9724 0.9588 0.9544 0.9680 0.9648 0.9684 0.9716 $\eta _{4}^{2}$ 0.9680 0.9572 0.9660 0.9612 0.9652 0.9724 0.9584 0.9584 0.9680 0.9648 0.9696 0.9716 $\eta _{5}^{2}$ 0.9676 0.9592 0.9656 0.9612 0.9652 0.9728 0.9576 0.9588 0.9680 0.9648 0.9704 0.9716 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9532 0.9668 0.9680 0.9620 0.9676 0.9724 0.9564 0.9560 0.9668 0.9588 0.9708 0.9692 $\eta _{2}^{2}$ 0.9524 0.9640 0.9680 0.9616 0.9672 0.9724 0.9568 0.9524 0.9664 0.9588 0.9688 0.9692 $\eta _{3}^{2}$ 0.9524 0.9636 0.9680 0.9616 0.9672 0.9728 0.9564 0.9520 0.9668 0.9588 0.9680 0.9692 $\eta _{4}^{2}$ 0.9532 0.9668 0.9680 0.9620 0.9676 0.9724 0.9564 0.9560 0.9668 0.9588 0.9708 0.9692 $\eta _{5}^{2}$ 0.9536 0.9672 0.9676 0.9620 0.9684 0.9720 0.9564 0.9580 0.9672 0.9588 0.9716 0.9692 (λ1, λ2) = (8, 9) N1 N2 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9548 0.9564 0.9620 0.9736 0.9752 0.9720 0.9680 0.9664 0.9720 0.9724 0.9744 0.9776 $\eta _{2}^{2}$ 0.9548 0.9556 0.9628 0.9736 0.9752 0.9716 0.9684 0.9656 0.9728 0.9724 0.9744 0.9776 $\eta _{3}^{2}$ 0.9548 0.9552 0.9628 0.9736 0.9752 0.9716 0.9684 0.9656 0.9736 0.9724 0.9744 0.9780 $\eta _{4}^{2}$ 0.9548 0.9564 0.9620 0.9736 0.9752 0.9720 0.9680 0.9664 0.9720 0.9724 0.9744 0.9776 $\eta _{5}^{2}$ 0.9548 0.9576 0.9624 0.9736 0.9756 0.9720 0.9680 0.9664 0.9720 0.9724 0.9748 0.9776 N3 N4 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9764 0.9676 0.9764 0.9668 0.9708 0.9776 0.9716 0.9680 0.9772 0.9704 0.9764 0.9796 $\eta _{2}^{2}$ 0.9764 0.9660 0.9764 0.9672 0.9704 0.9772 0.9720 0.9648 0.9776 0.9700 0.9756 0.9800 $\eta _{3}^{2}$ 0.9764 0.9656 0.9764 0.9672 0.9704 0.9772 0.9716 0.9640 0.9776 0.9700 0.9752 0.9800 $\eta _{4}^{2}$ 0.9764 0.9676 0.9764 0.9668 0.9708 0.9776 0.9716 0.9680 0.9772 0.9704 0.9764 0.9796 $\eta _{5}^{2}$ 0.9760 0.9684 0.9764 0.9668 0.9716 0.9776 0.9704 0.9696 0.9772 0.9704 0.9768 0.9796 N5 N6 Zmple Zmle Zmm Tmple Tmle Tmm Zmple Zmle Zmm Tmple Tmle Tmm $\eta _{1}^{2}$ 0.9692 0.9748 0.9780 0.9704 0.9748 0.9772 0.9692 0.9772 0.9836 0.9684 0.9788 0.9736 $\eta _{2}^{2}$ 0.9696 0.9732 0.9784 0.9700 0.9736 0.9772 0.9656 0.9760 0.9876 0.9680 0.9768 0.9736 $\eta _{3}^{2}$ 0.9696 0.9732 0.9784 0.9704 0.9736 0.9772 0.9656 0.9764 0.9809 0.9680 0.9768 0.9736 $\eta _{4}^{2}$ 0.9692 0.9748 0.9780 0.9704 0.9748 0.9772 0.9692 0.9772 0.9863 0.9684 0.9788 0.9736 $\eta _{5}^{2}$ 0.9696 0.9756 0.9784 0.9704 0.9756 0.9772 0.9700 0.9772 0.9868 0.9684 0.9800 0.9732