多个偏正态总体共同位置参数的Bootstrap置信区间

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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