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 5 三个总体时六种Bootstrap置信区间的模拟区间长度

(λ₁, λ₂, λ₃) = (3, 3, 4)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.1558	0.1979	0.1365	4.3721	6.2373	4.0877	0.1325	0.1794	0.1215	3.7023	5.2625	3.3734
$\eta _{2}^{2}$	0.3006	0.3512	0.2418	7.7139	11.0764	7.2551	0.2495	0.3182	0.2154	6.4917	9.3478	5.9910
$\eta _{3}^{2}$	0.4433	0.5465	0.3751	13.3325	17.2881	11.3168	0.4046	0.4949	0.3343	12.2296	14.5935	9.3507
$\eta _{4}^{2}$	1.0154	1.0665	0.7290	26.7962	33.8652	22.1617	0.7806	0.9649	0.6497	24.4722	28.5907	18.3170
$\eta _{5}^{2}$	1.5271	1.7688	1.2130	40.0428	56.0040	36.6571	1.3446	1.6015	1.0812	35.8804	47.2769	30.2912
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.1100	0.1527	0.0994	3.0012	3.9181	2.4516	0.0906	0.1159	0.0733	2.3937	3.0532	1.8877
$\eta _{2}^{2}$	0.2372	0.2708	0.1761	4.7556	6.9595	4.3525	0.1882	0.2057	0.1300	3.8212	5.4245	3.3539
$\eta _{3}^{2}$	0.3379	0.4209	0.2729	9.1752	10.8646	6.7914	0.2753	0.3204	0.2019	6.8204	8.4705	5.2370
$\eta _{4}^{2}$	0.5451	0.8201	0.5295	16.6665	21.2852	13.3020	0.5376	0.6261	0.3929	12.8209	16.5977	10.2607
$\eta _{5}^{2}$	1.2405	1.3619	0.8823	25.6048	35.1967	21.9996	0.8750	1.0374	0.6532	19.8941	27.4422	16.9660
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0770	0.0981	0.0608	1.9892	2.3561	1.4262	0.0687	0.0822	0.0494	1.8176	2.0390	1.2296
$\eta _{2}^{2}$	0.1658	0.1740	0.1077	2.8175	4.1868	2.5327	0.1298	0.1459	0.0875	2.7334	3.6225	2.1837
$\eta _{3}^{2}$	0.2416	0.2708	0.1668	5.6525	6.5386	3.9525	0.1859	0.2270	0.1356	5.1862	5.6567	3.4092
$\eta _{4}^{2}$	0.4589	0.5281	0.3235	10.3481	12.8113	7.7421	0.4102	0.4424	0.2631	10.0297	11.0841	6.6801
$\eta _{5}^{2}$	0.8659	0.8764	0.5392	13.4808	21.1830	12.8039	0.6102	0.7345	0.4385	14.6270	18.3261	11.0449
(λ₁, λ₂, λ₃) = (5, 5, 6)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.1407	0.1878	0.1222	4.0248	5.8983	3.7440	0.1151	0.1632	0.1041	3.2368	4.6661	2.9283
$\eta _{2}^{2}$	0.2739	0.3332	0.2165	7.0974	10.4754	6.6448	0.2185	0.2894	0.1845	5.6653	8.2891	5.2006
$\eta _{3}^{2}$	0.4017	0.5182	0.3357	12.3715	16.3519	10.3646	0.3563	0.4498	0.2864	10.9406	12.9415	8.1174
$\eta _{4}^{2}$	0.9341	1.0101	0.6519	24.9148	32.0333	20.2967	0.6866	0.8763	0.5565	21.9479	25.3549	15.9014
$\eta _{5}^{2}$	1.3924	1.6771	1.0854	36.9300	52.9723	33.5725	1.1886	1.4554	0.9262	31.7051	41.9254	26.2962
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0887	0.1279	0.0788	2.6180	3.3553	2.0751	0.0700	0.0875	0.0532	2.1090	2.6020	1.6216
$\eta _{2}^{2}$	0.1993	0.2269	0.1396	4.0753	5.9608	3.6841	0.1517	0.1552	0.0943	3.3151	4.6228	2.8811
$\eta _{3}^{2}$	0.2792	0.3524	0.2163	8.1131	9.3072	5.7488	0.2185	0.2419	0.1463	6.0298	7.2186	4.4990
$\eta _{4}^{2}$	0.4309	0.6860	0.4192	14.5853	18.2361	11.2604	0.4269	0.4728	0.2844	11.2715	14.1454	8.8144
$\eta _{5}^{2}$	1.0506	1.1400	0.6993	22.1638	30.1523	18.6226	0.6914	0.7832	0.4732	17.3326	23.3868	14.5749
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0593	0.0720	0.0437	1.8513	2.0602	1.2781	0.0558	0.0614	0.0369	1.7059	1.8071	1.1257
$\eta _{2}^{2}$	0.1345	0.1277	0.0774	2.5730	3.6615	2.2697	0.1069	0.1089	0.0654	2.5355	3.2111	1.9992
$\eta _{3}^{2}$	0.1932	0.1988	0.1197	5.2713	5.7193	3.5423	0.1503	0.1695	0.1013	4.8778	5.0149	3.1219
$\eta _{4}^{2}$	0.3651	0.3879	0.2319	9.6019	11.2065	6.9387	0.3410	0.3304	0.1963	9.4261	9.8271	6.1179
$\eta _{5}^{2}$	0.7096	0.6436	0.3869	12.2461	18.5292	11.4749	0.4951	0.5484	0.3276	13.6283	16.2471	10.1146
(λ₁, λ₂, λ₃) = (6, 8, 9)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.1374	0.1851	0.1190	3.8328	5.6934	3.5617	0.1115	0.1595	0.1006	3.0461	4.4063	2.7456
$\eta _{2}^{2}$	0.2679	0.3283	0.2107	6.7565	10.1120	6.3209	0.2122	0.2828	0.1783	5.3267	7.8279	4.8761
$\eta _{3}^{2}$	0.3922	0.5104	0.3265	11.8395	15.7855	9.8587	0.3464	0.4395	0.2767	10.4123	12.2221	7.6110
$\eta _{4}^{2}$	0.9154	0.9943	0.6336	23.8733	30.9242	19.3057	0.6669	0.8558	0.5375	20.9130	23.9460	14.9098
$\eta _{5}^{2}$	1.3617	1.6516	1.0557	35.2072	51.1376	31.9339	1.1564	1.4220	0.8948	29.9936	39.5952	24.6560
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0846	0.1226	0.0748	2.4665	3.1207	1.9302	0.0671	0.0827	0.0503	2.0203	2.4502	1.5399
$\eta _{1}^{2}$	0.1922	0.2175	0.1324	3.8063	5.5448	3.4270	0.1465	0.1468	0.0890	3.1575	4.3532	2.7361
$\eta _{1}^{2}$	0.2680	0.3377	0.2051	7.6932	8.6588	5.3476	0.2104	0.2286	0.1381	5.7836	6.7979	4.2725
$\eta _{1}^{2}$	0.4091	0.6571	0.3973	13.7625	16.9670	10.4745	0.4109	0.4466	0.2685	10.7888	13.3214	8.3705
$\eta _{1}^{2}$	1.0145	1.0923	0.6630	20.8033	28.0523	17.3230	0.6651	0.7403	0.4467	16.5347	22.0240	13.8411
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0571	0.0680	0.0415	1.8026	1.9617	1.2330	0.0543	0.0586	0.0355	1.6661	1.7271	1.0921
$\eta _{2}^{2}$	0.1306	0.1207	0.0734	2.4866	3.4866	2.1896	0.1043	0.1040	0.0630	2.4648	3.0692	1.9394
$\eta _{3}^{2}$	0.1871	0.1879	0.1136	5.1367	5.4466	3.4172	0.1462	0.1618	0.0976	4.7677	4.7936	3.0287
$\eta _{4}^{2}$	0.3531	0.3666	0.2198	9.3385	10.6722	6.6937	0.3329	0.3155	0.1889	9.2105	9.3939	5.9356
$\eta _{5}^{2}$	0.6897	0.6083	0.3669	11.8101	17.6458	11.0699	0.4818	0.5237	0.3154	13.2715	15.5304	9.8127