多个偏正态总体共同位置参数的Bootstrap置信区间

Processing math: 100%

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