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 4 两个总体时六种Bootstrap置信区间的模拟区间长度

(λ₁, λ₂) = (3, 4)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0411	0.0221	0.0154	1.2987	1.0654	0.6986	0.0275	0.0201	0.0137	1.0710	0.9018	0.5738
$\eta _{2}^{2}$	0.1802	0.1991	0.1384	4.9169	6.6592	4.3665	0.1553	0.1808	0.1236	4.1442	5.6363	3.5863
$\eta _{3}^{2}$	0.4284	0.5529	0.3845	13.9794	17.0478	11.1784	0.4068	0.5022	0.3360	10.8372	14.4292	9.1810
$\eta _{4}^{2}$	0.8817	1.0838	0.7537	36.8349	52.2064	34.2320	0.8903	0.9845	0.6729	32.5810	44.1873	28.1151
$\eta _{5}^{2}$	1.3595	1.7916	1.2460	74.1995	106.5424	69.8603	1.4416	1.6275	1.1124	61.4367	90.1772	57.3771
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0252	0.0171	0.0112	0.8519	0.7178	0.4647	0.0383	0.0129	0.0083	0.5550	0.5160	0.3071
$\eta _{2}^{2}$	0.1485	0.1539	0.1009	3.2747	4.4861	2.9044	0.1147	0.1164	0.0746	2.5189	3.2254	1.9195
$\eta _{3}^{2}$	0.3626	0.4274	0.2802	9.6313	11.4847	7.4355	0.2774	0.3235	0.2072	6.4404	8.2571	4.9140
$\eta _{4}^{2}$	0.5683	0.8377	0.5493	26.9447	35.1702	22.7699	0.5835	0.6340	0.4062	21.0352	25.2859	15.0482
$\eta _{5}^{2}$	1.2108	1.3848	0.9080	48.5261	71.7750	46.4686	0.8832	1.0481	0.6715	32.1665	51.6033	30.7102
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0336	0.0110	0.0068	0.6014	0.3940	0.2379	0.0345	0.0092	0.0056	0.4908	0.3422	0.2053
$\eta _{2}^{2}$	0.0935	0.0986	0.0615	1.8589	2.4626	1.4867	0.1076	0.0826	0.0503	1.7424	2.1391	1.2834
$\eta _{3}^{2}$	0.2080	0.2740	0.1708	5.7627	6.3043	3.8061	0.2012	0.2295	0.1397	5.5726	5.4763	3.2856
$\eta _{4}^{2}$	0.4737	0.5371	0.3349	13.8291	19.3065	11.6555	0.3902	0.4499	0.2739	13.5280	16.7701	10.0614
$\eta _{5}^{2}$	0.8088	0.8878	0.5536	27.4740	39.4007	23.7863	0.6367	0.7437	0.4527	21.7438	34.2241	20.5332
(λ₁, λ₂) = (5, 6)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0394	0.0210	0.0138	1.2360	1.0023	0.6375	0.0255	0.0183	0.0118	0.9932	0.8023	0.5009
$\eta _{2}^{2}$	0.1646	0.1887	0.1243	4.5252	6.2645	3.9848	0.1372	0.1645	0.1064	3.6578	5.0143	3.1310
$\eta _{3}^{2}$	0.3848	0.5242	0.3452	12.9767	16.0372	10.2012	0.3566	0.4568	0.2956	9.5920	12.8368	8.0154
$\eta _{4}^{2}$	0.7964	1.0275	0.6766	33.7643	49.1118	31.2397	0.7917	0.8955	0.5795	28.7679	39.3111	24.5460
$\eta _{5}^{2}$	1.2185	1.6985	1.1185	67.9331	100.2271	63.7537	1.2786	1.4804	0.9579	53.6549	80.2260	50.0932
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0228	0.0143	0.0089	0.7857	0.6215	0.3957	0.0361	0.0098	0.0061	0.5066	0.4393	0.2632
$\eta _{2}^{2}$	0.1275	0.1287	0.0803	2.8605	3.8848	2.4733	0.0952	0.0879	0.0545	2.2166	2.7457	1.6448
$\eta _{3}^{2}$	0.3042	0.3575	0.2231	8.5709	9.9451	6.3316	0.2233	0.2441	0.1515	5.6665	7.0291	4.2107
$\eta _{4}^{2}$	0.4537	0.7008	0.4373	23.6974	30.4554	19.3897	0.4774	0.4785	0.2969	18.6652	21.5255	12.8946
$\eta _{5}^{2}$	1.0214	1.1585	0.7229	41.8990	62.1532	39.5704	0.7079	0.7911	0.4908	27.3300	43.9289	26.3153
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0319	0.0080	0.0049	0.5740	0.3437	0.2114	0.0331	0.0068	0.0042	0.4703	0.3005	0.1874
$\eta _{2}^{2}$	0.0777	0.0724	0.0444	1.6875	2.1483	1.3215	0.0953	0.0616	0.0375	1.6146	1.8781	1.1713
$\eta _{3}^{2}$	0.1642	0.2010	0.1233	5.3241	5.4997	3.3830	0.1670	0.1712	0.1042	5.2454	4.8079	2.9985
$\eta _{4}^{2}$	0.3879	0.3939	0.2416	12.4861	16.8425	10.3598	0.3232	0.3355	0.2043	12.5257	14.7231	9.1822
$\eta _{5}^{2}$	0.6670	0.6512	0.3994	24.7334	34.3722	21.1422	0.5259	0.5546	0.3377	19.6984	30.0466	18.7387
(λ₁, λ₂) = (8, 9)
	N1						N2
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0386	0.0204	0.0131	1.2039	0.9676	0.6056	0.0246	0.0174	0.0109	0.9618	0.7591	0.4681
$\eta _{2}^{2}$	0.1578	0.1837	0.1180	4.3248	6.0474	3.7849	0.1297	0.1563	0.0984	3.4612	4.7443	2.9255
$\eta _{3}^{2}$	0.3660	0.5103	0.3279	12.4635	15.4815	9.6895	0.3357	0.4342	0.2733	9.0888	12.1456	7.4894
$\eta _{4}^{2}$	0.7595	1.0002	0.6427	32.1929	47.4100	29.6727	0.7508	0.8511	0.5357	27.2271	37.1946	22.9350
$\eta _{5}^{2}$	1.1574	1.6535	1.0625	64.7261	96.7542	60.5558	1.2110	1.4069	0.8856	50.5105	75.9066	46.8056
	N3						N4
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0219	0.0131	0.0080	0.7570	0.5777	0.3643	0.0355	0.0088	0.0054	0.4892	0.4095	0.2485
$\eta _{2}^{2}$	0.1190	0.1178	0.0721	2.6816	3.6109	2.2768	0.0897	0.0788	0.0486	2.1073	2.5595	1.5533
$\eta _{3}^{2}$	0.2806	0.3272	0.2004	8.1129	9.2440	5.8287	0.2080	0.2188	0.1351	5.3869	6.5525	3.9764
$\eta _{4}^{2}$	0.4076	0.6413	0.3927	22.2950	28.3083	17.8497	0.4473	0.4288	0.2648	17.8090	20.0658	12.1772
$\eta _{5}^{2}$	0.9453	1.0601	0.6492	39.0370	57.7713	36.4275	0.6581	0.7089	0.4378	25.5826	40.9500	24.8510
	N5						N6
	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm	Zmple	Zmle	Zmm	Tmple	Tmle	Tmm
$\eta _{1}^{2}$	0.0314	0.0072	0.0045	0.5646	0.3261	0.2034	0.0329	0.0063	0.0039	0.4632	0.2855	0.1814
$\eta _{2}^{2}$	0.0738	0.0651	0.0404	1.6289	2.0381	1.2713	0.0928	0.0564	0.0347	1.5702	1.7846	1.1336
$\eta _{3}^{2}$	0.1535	0.1809	0.1123	5.1740	5.2176	3.2545	0.1599	0.1566	0.0965	5.1318	4.5686	2.9020
$\eta _{4}^{2}$	0.3669	0.3546	0.2201	12.0263	15.9787	9.9664	0.3092	0.3069	0.1891	12.1779	13.9902	8.8866
$\eta _{5}^{2}$	0.6322	0.5862	0.3639	23.7951	32.6094	20.3393	0.5028	0.5073	0.3126	18.9885	28.5507	18.1355