Table 2.
Bias and variance of FDR estimation: FDR is the estimated true value averaged over 100 simulations, TNR is the total number of rejections. Pt/Pe are p-values derived from the theoretical/empirical null distributions, EB is empirical Bayes ranking with local FDR based on the empirical null distribution. C0 is based on the 75% quantile.
| λ0 = 0, σ0 = 1, λ = 10 | |||||||||
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| TNR | 50 | 100 | 200 | ||||||
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| FDR | bias | stderr | FDR | bias | stderr | FDR | bias | stderr | |
| Pt | 0.019 | 0.003 | 0.006 | 0.049 | −0.002 | 0.009 | 0.119 | −0.004 | 0.017 |
| Pe | 0.019 | 0.006 | 0.008 | 0.049 | 0.004 | 0.015 | 0.119 | 0.008 | 0.027 |
| EB | 0.019 | 0.006 | 0.009 | 0.049 | 0.004 | 0.015 | 0.119 | 0.009 | 0.028 |
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| λ0 = 0.5, σ0 = 2, λ = 10 | |||||||||
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| TNR | 50 | 100 | 200 | ||||||
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| FDR | bias | stderr | FDR | bias | stderr | FDR | bias | stderr | |
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| Pt | 0.071 | −0.071 | 0.000 | 0.118 | −0.118 | 0.000 | 0.218 | −0.217 | 0.0001 |
| Pe | 0.071 | 0.013 | 0.041 | 0.118 | 0.020 | 0.057 | 0.218 | 0.027 | 0.083 |
| EB | 0.071 | 0.013 | 0.041 | 0.118 | 0.021 | 0.058 | 0.218 | 0.028 | 0.084 |
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| λ0 = 0.5, σ0 = 0.5, λ = 10 | |||||||||
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| TNR | 50 | 100 | 200 | ||||||
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| FDR | bias | stderr | FDR | bias | stderr | FDR | bias | stderr | |
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| Pt | 0.078 | 0.903 | 0.042 | 0.130 | 0.870 | 0.0001 | 0.224 | 0.776 | 0.0001 |
| Pe | 0.078 | 0.001 | 0.047 | 0.130 | 0.005 | 0.068 | 0.224 | 0.013 | 0.092 |
| EB | 0.077 | 0.001 | 0.047 | 0.130 | 0.005 | 0.068 | 0.224 | 0.014 | 0.093 |