Table 1.

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 1

		β1	β2	β3	β4	β5	β6
		1.3	−1.3	1	−0.5	0.5	−0.5
Oracle	ave	1.2978	−1.3036	1.0049	−0.4985	0.5033	−0.4943
	std	0.1221	0.1477	0.1505	0.1169	0.0966	0.1049
		0.1264	0.1510	0.1527	0.1212	0.0983	0.1052
	95%	0.9510	0.9540	0.9440	0.9540	0.9520	0.9450
Eff	ave	1.2980	−1.3046	1.0064	−0.4990	0.5040	−0.4936
	std	0.1280	0.1546	0.1567	0.1221	0.1000	0.1075
		0.1317	0.1588	0.1602	0.1264	0.1011	0.1084
	95%	0.9480	0.9380	0.9380	0.9440	0.9480	0.9510
Local	ave	1.3052	−1.2629	0.9687	−0.4988	0.5023	−0.4897
	std	0.1478	0.1736	0.1715	0.1393	0.1069	0.1153
dMAVE	ave	1.2599	−1.2933	1.0014	−0.4763	0.4984	−0.4935
	std	0.1932	0.1427	0.1550	0.1701	0.1368	0.1378
SIR	ave	1.3881	−1.1930	0.9261	−0.5968	0.4793	−0.4724
	std	0.1696	0.1522	0.1414	0.1489	0.0976	0.0995
DR	ave	0.9935	−0.2217	0.1930	−0.6863	0.1245	−0.1071
	std	0.6567	1.2305	1.0107	0.6411	0.3069	0.2999