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 2 Bivariate 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	0.664	0.667	0.679	0.685	0.690	0.693	0.695	0.697	0.698	0.699
ε^∗=0.050	0.666	0.637	0.638	0.639	0.641	0.642	0.642	0.643	0.644	0.644
ε^∗=0.075	0.670	0.617	0.610	0.608	0.606	0.606	0.605	0.605	0.605	0.605
ε^∗=0.100	0.675	0.604	0.590	0.584	0.581	0.578	0.577	0.576	0.575	0.574
ε^∗=0.125	0.682	0.594	0.573	0.564	0.559	0.555	0.553	0.551	0.550	0.548
ε^∗=0.150	0.691	0.588	0.560	0.547	0.539	0.534	0.530	0.528	0.526	0.524
ε^∗=0.175	0.699	0.586	0.554	0.539	0.530	0.524	0.520	0.517	0.515	0.513
ε^∗=0.200	0.718	0.586	0.544	0.524	0.512	0.504	0.498	0.493	0.490	0.487
ε^∗=0.225	0.738	0.592	0.542	0.517	0.502	0.492	0.485	0.479	0.475	0.471
ε^∗=0.250	0.759	0.603	0.545	0.515	0.497	0.485	0.476	0.469	0.464	0.460
ε^∗=0.275	0.784	0.620	0.553	0.518	0.497	0.482	0.471	0.463	0.457	0.452
ε^∗=0.300	0.815	0.647	0.572	0.530	0.503	0.485	0.472	0.462	0.454	0.448
ε^∗=0.325	0.847	0.681	0.598	0.550	0.518	0.496	0.480	0.468	0.458	0.450
ε^∗=0.350	0.882	0.728	0.639	0.584	0.546	0.520	0.500	0.484	0.472	0.462
ε^∗=0.375	0.915	0.784	0.695	0.635	0.592	0.560	0.535	0.516	0.500	0.487
ε^∗=0.400	0.943	0.842	0.763	0.702	0.655	0.619	0.590	0.566	0.546	0.530
ε^∗=0.425	0.971	0.914	0.859	0.811	0.769	0.732	0.701	0.673	0.650	0.629
ε^∗=0.450	0.987	0.960	0.933	0.905	0.879	0.853	0.830	0.807	0.786	0.766
	n =110	n =120	n =130	n =140	n =150	n =160	n =170	n =180	n =190	n =200
ε^∗=0.025	0.700	0.701	0.701	0.702	0.702	0.703	0.703	0.704	0.704	0.704
ε^∗=0.050	0.644	0.645	0.645	0.645	0.645	0.645	0.645	0.646	0.646	0.646
ε^∗=0.075	0.604	0.604	0.604	0.604	0.604	0.604	0.604	0.604	0.604	0.604
ε^∗=0.100	0.574	0.573	0.573	0.573	0.573	0.572	0.572	0.572	0.572	0.572
ε^∗=0.125	0.548	0.547	0.546	0.546	0.545	0.545	0.544	0.544	0.544	0.543
ε^∗=0.150	0.523	0.522	0.521	0.520	0.519	0.518	0.518	0.517	0.517	0.517
ε^∗=0.175	0.511	0.510	0.509	0.508	0.507	0.506	0.506	0.505	0.505	0.504
ε^∗=0.200	0.485	0.483	0.482	0.480	0.479	0.478	0.477	0.477	0.476	0.475
ε^∗=0.225	0.469	0.466	0.464	0.463	0.461	0.460	0.459	0.458	0.457	0.456
ε^∗=0.250	0.457	0.454	0.452	0.449	0.448	0.446	0.445	0.443	0.442	0.441
ε^∗=0.275	0.448	0.444	0.442	0.439	0.437	0.435	0.433	0.432	0.430	0.429
ε^∗=0.300	0.443	0.438	0.435	0.432	0.429	0.426	0.424	0.422	0.420	0.419
ε^∗=0.325	0.444	0.439	0.434	0.430	0.426	0.423	0.421	0.418	0.416	0.414
ε^∗=0.350	0.454	0.447	0.441	0.435	0.431	0.427	0.423	0.420	0.417	0.415
ε^∗=0.375	0.476	0.467	0.459	0.452	0.446	0.441	0.436	0.432	0.428	0.424
ε^∗=0.400	0.516	0.504	0.493	0.484	0.476	0.469	0.462	0.457	0.451	0.447
ε^∗=0.425	0.611	0.594	0.580	0.567	0.555	0.544	0.535	0.526	0.518	0.511
ε^∗=0.450	0.748	0.731	0.715	0.700	0.687	0.674	0.662	0.650	0.640	0.630

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