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. Author manuscript; available in PMC: 2024 Sep 10.
Published in final edited form as: Stat Med. 2023 Jun 14;42(20):3685–3698. doi: 10.1002/sim.9825

TABLE 3.

The bias, standard deviation (SD), standard error (SE), and the coverage probability of 95% confidence intervals (CP) of the estimators in Examples 1 to 3.

a^ β^1 β^2
Method MSE Bias SD SE CP Bias SD SE CP
Example 1 50 SCAD 0.022 0.011 0.043 0.045 95.0 0.012 0.043 0.045 95.0
FE 0.078 0.029 0.045 0.047 91.0 0.026 0.045 0.047 94.0
RE 0.189 0.005 0.044 0.046 97.0 0.008 0.044 0.046 95.0
Oracle 0.002 0.003 0.043 0.046 97.0 0.005 0.043 0.046 94.0
100 SCAD 0.017 0.002 0.034 0.032 93.0 0.004 0.033 0.032 94.0
FE 0.074 0.034 0.032 0.033 88.0 0.032 0.034 0.033 87.0
RE 0.034 0.001 0.032 0.033 95.0 0.001 0.033 0.033 94.0
Oracle 0.001 0.002 0.032 0.032 95.0 0.001 0.033 0.032 93.0
Example 2 50 SCAD 0.321 0.001 0.032 0.030 93.0 0.002 0.031 0.030 94.0
FE 1.183 0.002 0.033 0.030 93.0 0.002 0.031 0.030 94.0
RE 1.810 4e-4 0.032 0.030 94.0 0.003 0.031 0.030 94.0
100 SCAD 0.242 0.002 0.019 0.021 97.0 0.002 0.022 0.021 93.0
FE 1.080 0.001 0.020 0.021 98.0 0.003 0.022 0.021 93.0
RE 0.060 0.001 0.019 0.021 98.0 0.001 0.022 0.021 93.0
Example 3 50 SCAD 0.016 0.004 0.047 0.046 94.0 0.007 0.044 0.046 97.0
FE 0.079 0.031 0.046 0.047 90.0 0.027 0.045 0.047 92.0
RE 0.847 0.003 0.045 0.046 96.0 0.006 0.044 0.046 96.0
Oracle 0.003 9e-5 0.044 0.046 96.0 0.003 0.042 0.046 97.0
100 SCAD 0.012 0.001 0.033 0.032 94.0 1e-4 0.032 0.032 92.0
FE 0.077 0.035 0.032 0.033 88.0 0.034 0.033 0.032 89.0
RE 0.039 0.003 0.032 0.033 94.0 0.001 0.033 0.033 92.0
Oracle 0.001 0.003 0.032 0.032 94.0 0.002 0.033 0.032 92.0