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. 2017 Jan 3;104(1):31–50. doi: 10.1093/biomet/asw054

Table 4.

Empirical bias, empirical and estimated variances, coverages and mean squared errors for the realistic settings, for simex with three different extrapolation functions

      Simex (linear) Simex (quadratic) Simex (cubic)
Inline graphic Inline graphic Estimate Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
200 0.1 Bias 0.0 -3.0 -2.2 -1.4 -0.3 -2.2 -1.4 0.0 -2.2
    Emp. var. 12.0 19.2 6.7 12.4 20.6 6.7 12.5 21.2 6.7
    Est. Var. 10.2 17.9 6.3 10.7 19.1 6.3 11.0 19.4 6.3
    95% cv 93.6 95.6 94.8 93.4 96.2 94.8 93.2 95.0 94.4
    MSE 12.0 19.3 6.8 12.4 20.6 6.8 12.5 21.2 6.8
200 0.25 Bias 14.5 -32.5 -1.9 7.4 -18.6 -2.0 3.6 -10.6 -1.9
    Emp. var. 10.4 14.1 6.7 12.1 20.7 6.8 13.8 26.5 6.8
    Est. Var. 8.8 11.2 6.2 9.7 14.6 6.3 16.0 18.2 6.3
    95% cv 90.9 80.8 95.4 92.7 88.6 95.1 93.1 89.9 95.7
    MSE 12.5 24.7 6.7 12.6 24.2 6.8 14.0 27.6 6.9
300 0.1 Bias -1.1 -1.6 -1.3 -2.5 1.3 -1.3 -2.5 1.9 -1.2
    Emp. var. 9.5 15.2 4.3 9.8 16.4 4.3 10.8 17.1 4.3
    Est. Var. 8.0 11.8 4.1 7.6 12.5 4.1 7.8 12.8 4.1
    95% cv 92.8 93.8 95.6 92.8 93.8 95.6 92.8 93.6 95.4
    MSE 9.5 15.2 4.3 9.9 16.4 4.4 10.8 17.1 4.4
300 0.25 Bias 13.1 -30.0 -1.2 6.0 -15.8 -1.4 1.9 -6.8 -1.6
    Emp. var. 8.4 11.7 4.4 9.9 17.4 4.4 11.4 22.4 4.5
    Est. Var. 8.1 7.4 4.1 6.9 9.7 4.2 8.1 12.1 4.2
    95% cv 87.2 72.9 95.6 89.7 83.9 95.6 91.8 85.2 95.2
    MSE 10.1 20.7 4.4 10.3 19.9 4.4 11.4 22.9 4.5

Emp. var., empirical variance; Est. var., estimated variance; 95% cv, coverage probabilities of 95% confidence intervals computed based on the asymptotic normal distribution; MSE, mean squared error. All numbers were multiplied by 100.