. Author manuscript; available in PMC: 2014 Apr 28.

Published in final edited form as: J Am Stat Assoc. 2013 Apr 28;108(503):10.1080/01621459.2013.794730. doi: 10.1080/01621459.2013.794730

Table 2.

Numerical validation of the proposed sandwich estimator in the parameter cascading method when the data noise has the standard deviation σ = 0.02, 0.05. Under each scenario, the first two rows are means of 1000 sandwich and bootstrap standard error $(\hat{S E})$ estimators obtained from the same 1000 simulated data sets, respectively; the last row is the sample standard deviation of 1000 parameter estimates obtained from the same 1000 simulated data sets.

Parameters

θ_D

θ_S

θ_A

σ = 0.02

\hat{S E}

Mean of Sandwich Estimators

0.0246

0.00375

0.000467

Mean of Bootstrap Estimators

0.0257

0.00374

0.000474

Sample Standard Deviation

0.0249

0.00375

0.000465

σ = 0.05

\hat{S E}

Mean of Sandwich Estimators

0.0392

0.00599

0.000783

Mean of Bootstrap Estimators

0.0404

0.00597

0.000791

Sample Standard Deviation

0.0405

0.00617

0.000795