Table 3.

The average (“ave”) and the sample standard errors (“std”) for various estimates, and the inference results, respectively, the average of the estimated standard deviation (“ $\widehat{\text{std}}$”) and the coverage of the estimated 95% confidence interval (“95%”), of the oracle estimator and the efficient estimator, of β in simulated example 3

		β11	β21	β31	β41	β51	β61	β12	β22	β32	β42	β52	β62
		1	0.6667	0.6667	0	−0.3333	0.6667	0.8	0.8	−0.3	0.3	0	0
Oracle	ave	1.0009	0.6676	0.6674	0.0002	−0.3339	0.6675	0.8064	0.8064	−0.2905	0.2969	−0.0047	0.0053
	std	0.0305	0.0305	0.0325	0.0099	0.0198	0.0314	0.0860	0.0860	0.0902	0.0291	0.0550	0.0854
		0.0275	0.0275	0.0295	0.0109	0.0178	0.0276	0.0828	0.0828	0.0876	0.0296	0.0547	0.0826
	95%	0.9270	0.9270	0.9300	0.9590	0.9200	0.9110	0.9410	0.9410	0.9320	0.9450	0.9520	0.9430
Eff	ave	1.0097	0.6763	0.6764	−0.0000	−0.3384	0.6752	0.8038	0.8038	−0.3067	0.3105	0.0022	−0.0003
	std	0.0714	0.0714	0.0745	0.0162	0.0434	0.0740	0.1737	0.1737	0.1993	0.0485	0.1511	0.1895
		0.0709	0.0709	0.0734	0.0175	0.0454	0.0702	0.1439	0.1439	0.1490	0.0381	0.0973	0.1439
	95%	0.9280	0.9280	0.9350	0.9530	0.9460	0.9430	0.9230	0.9230	0.9240	0.9410	0.9150	0.9080
local	ave	1.0633	0.7300	0.7372	−0.0072	−0.3701	0.7468	0.7689	0.7689	−0.3066	0.2754	−0.0116	−0.0042
	std	1.8783	1.8783	2.1273	0.2493	1.0694	2.3913	1.1281	1.1281	1.5767	0.4517	0.2192	0.2516
dMAVE	ave	0.8884	0.6079	−0.1703	0.2119	−0.2498	0.5065	0.8282	0.7722	−0.0901	0.2371	−0.0153	0.0354
	std	0.0748	0.1021	0.0951	0.0569	0.0888	0.1155	0.0379	0.0378	0.1188	0.0731	0.0761	0.0489
SIR	ave	0.5443	0.3781	−0.3301	0.1816	−0.0944	0.1976	0.7768	0.6849	−0.4083	0.2908	0.0441	−0.0828
	std	0.1514	0.1414	0.0863	0.0586	0.1257	0.2022	0.0650	0.0808	0.1098	0.0748	0.1059	0.0831
DR	ave	0.6332	0.2753	−0.2968	0.0939	−0.2701	0.5422	0.7004	0.6823	−0.4512	0.1498	0.0013	−0.0151
	std	0.1813	0.2009	0.1003	0.0739	0.1288	0.1567	0.1063	0.1446	0.1688	0.0880	0.1639	0.0945