Table 3.

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 the cutoff values, $c_1$ and $c_2$, for each of the explored approaches.

Method	Approach	${\mathit{n}}_1,{\mathit{n}}_2,{\mathit{n}}_3$	${\mathit{c}}_1$			${\mathit{c}}_2$
			Bias	Variance	MSE	Bias	Variance	MSE
Euclidean	Logistic	$\mathrm{30,30,30}$	−0.1126	0.2018	0.2145	−0.4859	0.4447	0.6808
		$\mathrm{50,50,50}$	−0.0635	0.1452	0.1492	−0.2957	0.3222	0.4097
		$\mathrm{100,100,100}$	−0.0189	0.1017	0.1021	−0.1446	0.2212	0.2421
		$\mathrm{200,200,200}$	−0.0099	0.0605	0.0606	−0.0420	0.1537	0.1554
		$\mathrm{200,50,50}$	0.0623	0.1160	0.1199	−0.1816	0.2937	0.3267
	Yan	$\mathrm{30,30,30}$	−0.1907	0.1010	0.1374	−0.7236	0.5345	1.0581
		$\mathrm{50,50,50}$	−0.1439	0.0696	0.0904	−0.4901	0.4182	0.6583
		$\mathrm{100,100,100}$	−0.0826	0.0460	0.0528	−0.2498	0.2852	0.3476
		$\mathrm{200,200,200}$	−0.0454	0.0304	0.0325	−0.0805	0.2173	0.2237
		$\mathrm{200,50,50}$	−0.0896	0.0570	0.0650	−0.3962	0.4245	0.5815
	Normal	$\mathrm{30,30,30}$	−0.1024	0.0572	0.0677	−0.4509	0.3104	0.5137
		$\mathrm{50,50,50}$	−0.0719	0.0388	0.0439	−0.2877	0.2489	0.3317
		$\mathrm{100,100,100}$	−0.0305	0.0217	0.0226	−0.1132	0.1664	0.1793
		$\mathrm{200,200,200}$	−0.0131	0.0126	0.0127	−0.0360	0.1122	0.1135
		$\mathrm{200,50,50}$	−0.0400	0.0244	0.0260	−0.2202	0.2193	0.2678
	Stepwise	$\mathrm{30,30,30}$	−0.0888	0.0771	0.0850	−1.1444	0.4898	1.7995
		$\mathrm{50,50,50}$	−0.1860	0.1141	0.1487	−0.9142	0.4116	1.2474
		$\mathrm{100,100,100}$	−0.0135	0.0625	0.0626	−0.5736	0.3859	0.7149
		$\mathrm{200,200,200}$	0.0080	0.0507	0.0508	−0.3582	0.3197	0.4480
		$\mathrm{200,50,50}$	0.0335	0.0686	0.0697	−0.7967	0.4410	1.0758
Youden	Logistic	$\mathrm{30,30,30}$	−0.3275	0.3552	0.4625	−0.4990	0.5443	0.7933
		$\mathrm{50,50,50}$	−0.1939	0.2692	0.3068	−0.3365	0.3918	0.5050
		$\mathrm{100,100,100}$	−0.1157	0.2015	0.2149	−0.1453	0.2712	0.2924
		$\mathrm{200,200,200}$	−0.0789	0.1285	0.1347	−0.0569	0.2111	0.2144
		$\mathrm{200,50,50}$	−0.0069	0.2303	0.2304	−0.1971	0.4077	0.4465
	Yan	$\mathrm{30,30,30}$	−0.2819	0.2030	0.2825	−0.6182	0.5326	0.9148
		$\mathrm{50,50,50}$	−0.1792	0.1604	0.1925	−0.4075	0.4043	0.5703
		$\mathrm{100,100,100}$	−0.0955	0.0985	0.1076	−0.2411	0.2817	0.3398
		$\mathrm{200,200,200}$	−0.0362	0.0659	0.0672	−0.0708	0.2235	0.2285
		$\mathrm{200,50,50}$	−0.1088	0.1325	0.1444	−0.3358	0.4329	0.5456
	Normal	$\mathrm{30,30,30}$	−0.1589	0.0871	0.1123	−0.3372	0.2840	0.3977
		$\mathrm{50,50,50}$	−0.1138	0.0597	0.0726	−0.2213	0.2140	0.2630
		$\mathrm{100,100,100}$	−0.0476	0.0346	0.0369	−0.0851	0.1394	0.1466
		$\mathrm{200,200,200}$	−0.0179	0.0195	0.0198	−0.0200	0.0939	0.0943
		$\mathrm{200,50,50}$	−0.0707	0.0431	0.0481	−0.1468	0.1892	0.2107
	Stepwise	$\mathrm{30,30,30}$	−0.4349	0.2281	0.4173	−1.1462	0.4646	1.7782
		$\mathrm{50,50,50}$	−0.3295	0.1957	0.3043	−0.8778	0.4531	1.2236
		$\mathrm{100,100,100}$	−0.2084	0.1767	0.2201	−0.6420	0.3861	0.7983
		$\mathrm{200,200,200}$	−0.1550	0.1200	0.1440	−0.3821	0.3118	0.4578
		$\mathrm{200,50,50}$	−0.1716	0.1746	0.2040	−0.7022	0.5060	0.9991