Table 2.

The table provides results for the normal scenarios with $\mathbf{\Sigma }=0.7\mathit{I}+0.3\mathit{J}$. Included are the bias, variance, and MSE for ${\hat{\beta }}_1,{\hat{\beta }}_2$ and ${\hat{\beta }}_3$ for each of the explored approaches.

Method	Approach	${\mathit{n}}_1,{\mathit{n}}_2,{\mathit{n}}_3$	${\stackrel{\mathit{ˆ}}{\mathit{\beta }}}_1$			${\stackrel{\mathit{ˆ}}{\mathit{\beta }}}_2$			${\stackrel{\mathit{ˆ}}{\mathit{\beta }}}_3$
			Bias	Variance	MSE	Bias	Variance	MSE	Bias	Variance	MSE
Euclidean	Logistic	$\mathrm{30,30,30}$	−0.0506	0.0766	0.0792	−0.0607	0.0596	0.0633	−0.1131	0.0336	0.0464
		$\mathrm{50,50,50}$	−0.0238	0.0567	0.0572	−0.0451	0.0464	0.0484	−0.0741	0.0191	0.0246
		$\mathrm{100,100,100}$	−0.0133	0.0334	0.0336	−0.0111	0.0275	0.0276	−0.0334	0.0060	0.0071
		$\mathrm{200,200,200}$	0.0000	0.0194	0.0194	−0.0003	0.0171	0.0171	−0.0134	0.0017	0.0019
		$\mathrm{200,50,50}$	−0.0082	0.0397	0.0397	−0.0290	0.0317	0.0325	−0.0426	0.0086	0.0104
	Yan	$\mathrm{30,30,30}$	−0.0923	0.1469	0.1554	−0.1414	0.1176	0.1376	−0.1928	0.0815	0.1187
		$\mathrm{50,50,50}$	−0.0485	0.1129	0.1153	−0.0942	0.0862	0.0951	−0.1547	0.0514	0.0753
		$\mathrm{100,100,100}$	−0.0365	0.0710	0.0723	−0.0346	0.0547	0.0559	−0.0837	0.0231	0.0301
		$\mathrm{200,200,200}$	−0.0024	0.0484	0.0484	−0.0073	0.0376	0.0377	−0.0471	0.0109	0.0131
		$\mathrm{200,50,50}$	−0.0384	0.1029	0.1044	−0.0814	0.0828	0.0894	−0.1274	0.0460	0.0622
	Normal	$\mathrm{30,30,30}$	−0.0547	0.0825	0.0855	−0.0759	0.0657	0.0715	−0.1288	0.0391	0.0557
		$\mathrm{50,50,50}$	−0.0297	0.0633	0.0642	−0.0539	0.0514	0.0543	−0.0843	0.0224	0.0295
		$\mathrm{100,100,100}$	−0.0160	0.0364	0.0367	−0.0123	0.0302	0.0303	−0.0374	0.0068	0.0082
		$\mathrm{200,200,200}$	−0.0016	0.0219	0.0219	−0.0020	0.0182	0.0182	−0.0157	0.0022	0.0024
		$\mathrm{200,50,50}$	−0.0168	0.0540	0.0543	−0.0501	0.0437	0.0463	−0.0643	0.0147	0.0189
	Stepwise	$\mathrm{30,30,30}$	−0.1768	0.1607	0.1920	−0.2366	0.1487	0.2047	−0.2681	0.1145	0.1864
		$\mathrm{50,50,50}$	−0.1207	0.1415	0.1561	−0.1767	0.1238	0.1550	−0.2349	0.0834	0.1386
		$\mathrm{100,100,100}$	−0.0937	0.1220	0.1308	−0.1051	0.0845	0.0956	−0.1532	0.0481	0.0716
		$\mathrm{200,200,200}$	−0.0391	0.0915	0.0930	−0.0697	0.0670	0.0718	−0.1170	0.0316	0.0452
		$\mathrm{200,50,50}$	−0.1271	0.1364	0.1525	−0.1542	0.1120	0.1358	−0.2041	0.0754	0.1170
Youden	Logistic	$\mathrm{30,30,30}$	−0.0506	0.0766	0.0792	−0.0607	0.0596	0.0633	−0.1131	0.0336	0.0464
		$\mathrm{50,50,50}$	−0.0238	0.0567	0.0572	−0.0451	0.0464	0.0484	−0.0741	0.0191	0.0246
		$\mathrm{100,100,100}$	−0.0133	0.0334	0.0336	−0.0111	0.0275	0.0276	−0.0334	0.0060	0.0071
		$\mathrm{200,200,200}$	0.0000	0.0194	0.0194	−0.0003	0.0171	0.0171	−0.0134	0.0017	0.0019
		$\mathrm{200,50,50}$	−0.0082	0.0397	0.0397	−0.0290	0.0317	0.0325	−0.0426	0.0086	0.0104
	Yan	$\mathrm{30,30,30}$	−0.0907	0.1334	0.1416	−0.1294	0.1076	0.1244	−0.1897	0.0793	0.1153
		$\mathrm{50,50,50}$	−0.0387	0.1071	0.1086	−0.0851	0.0850	0.0922	−0.1460	0.0468	0.0681
		$\mathrm{100,100,100}$	−0.0376	0.0677	0.0691	−0.0379	0.0541	0.0555	−0.0788	0.0224	0.0286
		$\mathrm{200,200,200}$	0.0070	0.0522	0.0523	−0.0033	0.0363	0.0363	−0.0478	0.0110	0.0133
		$\mathrm{200,50,50}$	−0.0324	0.0976	0.0987	−0.0792	0.0793	0.0856	−0.1168	0.0425	0.0561
	Normal	$\mathrm{30,30,30}$	−0.0482	0.0792	0.0815	−0.0657	0.0618	0.0661	−0.1187	0.0348	0.0489
		$\mathrm{50,50,50}$	−0.0252	0.0583	0.0590	−0.0490	0.0481	0.0505	−0.0767	0.0195	0.0254
		$\mathrm{100,100,100}$	−0.0148	0.0337	0.0340	−0.0110	0.0286	0.0287	−0.0337	0.0058	0.0070
		$\mathrm{200,200,200}$	−0.0005	0.0196	0.0196	0.0003	0.0171	0.0171	−0.0137	0.0018	0.0020
		$\mathrm{200,50,50}$	−0.0104	0.0482	0.0483	−0.0411	0.0390	0.0406	−0.0546	0.0120	0.0150
	Stepwise	$\mathrm{30,30,30}$	−0.2503	0.1613	0.2240	−0.2243	0.1435	0.1938	−0.2661	0.1114	0.1823
		$\mathrm{50,50,50}$	−0.1853	0.1420	0.1763	−0.1876	0.1171	0.1523	−0.2164	0.0836	0.1304
		$\mathrm{100,100,100}$	−0.1498	0.1123	0.1347	−0.1229	0.0780	0.0931	−0.1410	0.0448	0.0647
		$\mathrm{200,200,200}$	−0.0922	0.0845	0.0930	−0.0658	0.0550	0.0594	−0.0949	0.0246	0.0336
		$\mathrm{200,50,50}$	−0.1407	0.1278	0.1476	−0.1487	0.1025	0.1246	−0.1708	0.0610	0.0902