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. Author manuscript; available in PMC: 2010 May 25.
Published in final edited form as: Biometrics. 2009 May 4;66(1):149–158. doi: 10.1111/j.1541-0420.2009.01260.x

Table 1.

Summary of simulation results on parametric and semiparametric estimation of β in model (1) of log X = −βTZ + ε.

fξ(·)†: Lognormal
 fξ(·)†: Weibull
β n Estimation‡ Bias 95% CP SE Mean SE Bias 95% CP SE Mean SE
0 50 Para-L −0.0003 0.959 0.5031 0.5037 0.0092 0.831 0.3387 0.2437
Para-W 0.0123 0.853 0.6017 0.4911 0.0002 0.954 0.2297 0.2294
Semi-L 0.0006 0.951 0.7657 0.7651 0.0001 0.950 0.7899 0.7901
Semi-G 0.0002 0.955 0.6533 0.6534 −0.0003 0.951 0.5084 0.5085
200 Lognormal 0.0002 0.945 0.2540 0.2539 0.0096 0.837 0.1779 0.1271
Weibull 0.0125 0.859 0.3152 0.2436 0.0002 0.955 0.1096 0.1095
Semi-L 0.0003 0.947 0.3897 0.3899 −0.0006 0.948 0.3973 0.3974
Semi-G 0.0004 0.952 0.3261 0.3261 −0.0002 0.950 0.2603 0.2601
500 Lognormal −0.0001 0.949 0.1565 0.1564 0.0098 0.832 0.1195 0.0814
Weibull 0.0121 0.857 0.2049 0.1537 −0.0002 0.951 0.0716 0.0718
Semi-L 0.0002 0.950 0.2504 0.2503 −0.0002 0.950 0.2472 0.2470
Semi-G −0.0001 0.950 0.2477 0.2479 −0.0003 0.949 0.1619 0.1619
1 50 Lognormal −0.0045 0.942 0.5023 0.5021 0.0091 0.831 0.3391 0.2471
Weibull 0.0122 0.851 0.6297 0.4731 −0.0001 0.947 0.2348 0.2347
Semi-L 0.0005 0.951 0.5451 0.5453 −0.0007 0.952 0.5411 0.5409
Semi-G −0.0002 0.954 0.5227 0.5225 0.0001 0.951 0.4603 0.4605
200 Lognormal 0.0002 0.951 0.2511 0.2510 0.0093 0.830 0.1903 0.1275
Weibull 0.0120 0.856 0.3111 0.2419 −0.0005 0.951 0.1198 0.1198
Semi-L 0.0009 0.950 0.2751 0.2750 −0.0001 0.951 0.2755 0.2754
Semi-G −0.0003 0.951 0.2603 0.2602 −0.0001 0.949 0.2443 0.2445
500 Lognormal −0.0000 0.951 0.1628 0.1627 0.0096 0.833 0.1168 0.0809
Weibull 0.0124 0.852 0.2081 0.1541 0.0003 0.950 0.0716 0.0716
Semi-L −0.0001 0.949 0.1689 0.1690 0.0001 0.949 0.1697 0.1698
Semi-G 0.0002 0.951 0.1654 0.1653 −0.0000 0.951 0.1447 0.1448
†

fξ(·): true density function of ξ = exp(ε)

‡

Estimation: Para-L, parametric estimation using Lognormal distribution; Para-W, parametric estimation using Weibull distribution; Semi-L, semiparametric estimation without weight function; Semi-G, semiparametric estimation using Gehan weight function