. Author manuscript; available in PMC: 2010 Mar 1.

Published in final edited form as: J Am Stat Assoc. 2005 Mar 1;100(469):296–309. doi: 10.1198/016214504000000818.

Table 2.

Efficiencies (relative to of the UMVU estimator ${\hat{σ}}_{U M V U}^{2}$ ) of the different variance estimators for different combinations of p, Δ, and n. For the limiting Bayes and weighted estimators, the values are based on simulation studies with 10000 replications for each combination.

Combinations of p and Δ		Efficiency %
Combinations of p and Δ	n	MRE	pMLE	pMRE	ALB	LB1	LB2	LB3	LB4	PLB1	PLB2	PLB3

	3	200	174	222	14	10	60	152	230	240	236	233
Δ=(−0.25,0,0.25)	10	122	117	124	71	62	89	113	128	129	129	128
p=3	30	107	106	107	91	89	99	107	105	112	112	112

	3	200	183	209	17	11	66	160	217	235	226	221
Δ=(−0.5,0,0.5)	10	122	119	124	73	59	86	110	127	129	128	127
p=3	30	107	106	110	89	84	95	104	109	111	111	111

	3	200	164	226	13	9	51	135	227	238	234	232
Δ=(0,0.25, 0.50)	10	122	114	127	66	53	78	103	131	129	128	128
p=3	30	107	105	109	88	81	92	100	107	108	108	108

	3	200	166	222	13	8	47	128	222	233	228	224
Δ=(0,0.5,1)	10	122	115	128	65	51	76	102	126	126	126	126
p=3	30	107	105	110	87	83	94	103	109	110	110	110

	3	200	174	222	14	10	58	149	234	241	238	235
Δ=(−0.25:2⁻⁴:0.25)	10	122	117	123	71	61	88	112	127	130	130	129
p=9	30	107	105	106	91	88	98	106	109	111	111	111

	3	200	174	222	14	10	57	145	234	239	237	234
Δ=(−0.25:2⁻⁵:0.25)	10	122	117	123	71	60	86	109	130	127	127	126
p=17	30	107	105	106	91	87	97	105	108	110	110	110

	3	200	164	225	13	9	52	137	230	243	240	238
Δ=(0:2⁻⁴:0.5)	10	122	114	126	66	53	77	102	129	128	127	127
p=9	30	107	104	108	88	76	87	97	109	107	107	107

	3	200	164	225	13	10	55	145	235	249	246	243
Δ=(0:2⁻⁵:0.5)	10	122	114	126	66	54	79	106	130	134	133	133
p=17	30	107	104	108	88	76	87	97	111	107	107	108