Table 3.

Summary of simulation results. Comparison between the inclusion probabilities and local averages. The covariate is uniformly distributed on five points, m/5, 1 < m < 5.

n	β 0	ñ	τ θ	Approach	Mean ${\widehat{\beta }}^{\ast }$	Proposed s.e.	True S.D.	95% coverage
1000	0	366	0.83	Inclusion probabilities	0.004	0.2407	0.2399	0.949
				Local average	–0.004	0.2214	0.2251	0.945
		367	0.43	Inclusion probabilities	0.001	0.2728	0.2703	0.949
				Local average	0.001	0.2624	0.2674	0.944
		367	0.29	Inclusion probabilities	0.002	0.2779	0.2803	0.953
				Local average	0.004	0.2682	0.2779	0.948
		366	0.09	Inclusion probabilities	–0.006	0.2846	0.2845	0.954
				Local average	–0.009	0.2759	0.2816	0.943
	log(2)	364	0.83	Inclusion probabilities	0.702	0.2478	0.2503	0.950
				Local average	0.699	0.2288	0.2343	0.944
		364	0.43	Inclusion probabilities	0.702	0.2821	0.2864	0.946
				Local average	0.693	0.2708	0.2800	0.940
		364	0.29	Inclusion probabilities	0.706	0.2866	0.2899	0.948
				Local average	0.692	0.2760	0.2839	0.943
		364	0.09	Inclusion probabilities	0.710	0.2928	0.2981	0.952
				Local average	0.697	0.2835	0.2875	0.952
2000	0	734	0.83	Inclusion probabilities	–0.001	0.1697	0.1712	0.949
				Local average	–0.000	0.1568	0.1571	0.949
		734	0.43	Inclusion probabilities	0.004	0.1930	0.1883	0.956
				Local average	0.003	0.1866	0.1839	0.954
		733	0.29	Inclusion probabilities	–0.000	0.1961	0.1940	0.956
				Local average	–0.002	0.1903	0.1912	0.951
		734	0.09	Inclusion probabilities	–0.001	0.2002	0.1962	0.957
				Local average	–0.005	0.1955	0.1946	0.952
	log(2)	729	0.83	Inclusion probabilities	0.693	0.1747	0.1761	0.948
				Local average	0.696	0.1621	0.1641	0.946
		728	0.43	Inclusion probabilities	0.691	0.1992	0.2027	0.943
				Local average	0.695	0.1928	0.1943	0.945
		728	0.29	Inclusion probabilities	0.690	0.2023	0.2052	0.953
				Local average	0.694	0.1966	0.1990	0.945
		728	0.09	Inclusion probabilities	0.692	0.2070	0.2104	0.951
				Local average	0.692	0.2020	0.2062	0.946