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 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