Unbiased bootstrap error estimation for linear discriminant analysis

Vu, Thang; Sima, Chao; Braga-Neto, Ulisses M; Dougherty, Edward R

doi:10.1186/s13637-014-0015-0

EURASIP Journal on Bioinformatics and Systems Biology

Table 1 Univariate case: required weight w ^∗ for unbiased convex bootstrap estimation

From: Unbiased bootstrap error estimation for linear discriminant analysis

	n=10	n=20	n=30	n=40	n=50	n=60	n=70	n=80	n=90	n=100
ε^∗=0.025	0.724	0.687	0.679	0.675	0.674	0.672	0.671	0.671	0.670	0.670
ε^∗=0.050	0.736	0.696	0.685	0.680	0.678	0.676	0.674	0.673	0.672	0.672
ε^∗=0.075	0.738	0.701	0.689	0.683	0.679	0.677	0.676	0.674	0.674	0.673
ε^∗=0.100	0.729	0.704	0.691	0.684	0.681	0.678	0.677	0.675	0.674	0.673
ε^∗=0.125	0.708	0.701	0.692	0.686	0.682	0.679	0.677	0.676	0.675	0.674
ε^∗=0.150	0.681	0.692	0.693	0.687	0.683	0.680	0.678	0.677	0.676	0.675
ε^∗=0.175	0.646	0.670	0.688	0.687	0.683	0.680	0.678	0.677	0.676	0.675
ε^∗=0.200	0.625	0.631	0.673	0.683	0.683	0.681	0.679	0.677	0.676	0.675
ε^∗=0.225	0.614	0.574	0.639	0.671	0.679	0.680	0.679	0.677	0.676	0.675
ε^∗=0.250	0.617	0.516	0.579	0.635	0.663	0.673	0.676	0.677	0.676	0.675
ε^∗=0.275	0.641	0.470	0.498	0.563	0.617	0.648	0.664	0.671	0.673	0.674
ε^∗=0.300	0.676	0.459	0.425	0.464	0.523	0.577	0.616	0.641	0.656	0.665
ε^∗=0.325	0.724	0.487	0.393	0.379	0.405	0.451	0.502	0.548	0.587	0.614
ε^∗=0.350	0.780	0.549	0.422	0.356	0.331	0.334	0.356	0.389	0.428	0.469
ε^∗=0.375	0.837	0.639	0.505	0.412	0.350	0.310	0.288	0.280	0.282	0.295
ε^∗=0.400	0.890	0.741	0.626	0.533	0.458	0.398	0.350	0.312	0.283	0.261
ε^∗=0.425	0.935	0.842	0.761	0.690	0.627	0.570	0.519	0.474	0.434	0.399
ε^∗=0.450	0.971	0.925	0.884	0.845	0.808	0.772	0.739	0.707	0.676	0.647
	n =110	n =120	n =130	n =140	n =150	n =160	n =170	n =180	n =190	n =200
ε^∗=0.025	0.669	0.669	0.669	0.669	0.669	0.669	0.669	0.668	0.668	0.668
ε^∗=0.050	0.671	0.671	0.671	0.671	0.670	0.670	0.670	0.669	0.670	0.669
ε^∗=0.075	0.672	0.672	0.671	0.671	0.671	0.671	0.670	0.670	0.670	0.670
ε^∗=0.100	0.673	0.672	0.672	0.671	0.671	0.671	0.671	0.670	0.670	0.670
ε^∗=0.125	0.673	0.673	0.672	0.672	0.672	0.671	0.671	0.671	0.670	0.670
ε^∗=0.150	0.674	0.673	0.673	0.672	0.672	0.672	0.671	0.671	0.671	0.671
ε^∗=0.175	0.674	0.673	0.673	0.672	0.672	0.672	0.672	0.671	0.671	0.671
ε^∗=0.200	0.674	0.673	0.673	0.673	0.672	0.672	0.672	0.671	0.671	0.671
ε^∗=0.225	0.675	0.674	0.673	0.672	0.672	0.672	0.672	0.672	0.671	0.671
ε^∗=0.250	0.675	0.674	0.673	0.673	0.672	0.672	0.672	0.672	0.671	0.671
ε^∗=0.275	0.674	0.674	0.673	0.673	0.673	0.673	0.672	0.671	0.671	0.671
ε^∗=0.300	0.669	0.671	0.672	0.672	0.672	0.672	0.672	0.672	0.672	0.672
ε^∗=0.325	0.635	0.648	0.657	0.663	0.666	0.668	0.669	0.670	0.671	0.671
ε^∗=0.350	0.508	0.543	0.572	0.597	0.615	0.630	0.642	0.649	0.655	0.660
ε^∗=0.375	0.313	0.337	0.365	0.394	0.425	0.455	0.484	0.511	0.536	0.557
ε^∗=0.400	0.245	0.234	0.229	0.228	0.229	0.235	0.243	0.254	0.268	0.283
ε^∗=0.425	0.367	0.338	0.313	0.290	0.270	0.253	0.238	0.224	0.213	0.203
ε^∗=0.450	0.620	0.594	0.569	0.545	0.522	0.501	0.480	0.461	0.442	0.424

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