Comparing Parametric, Nonparametric, and Semiparametric Estimators: The Weibull Trials

A simple example is used to show how the bias and standard error of an estimator depend in part on the type of estimator chosen from among parametric, nonparametric, and semiparametric candidates. We estimate the cumulative distribution function in the presence of missing data with and without an auxiliary variable. Simulation results mirror theoretical expectations about the bias and precision of candidate estimators. Specifically, parametric maximum likelihood estimators performed best, but must be “omnisciently” correctly specified. An augmented inverse probability weighted (IPW) semiparametric estimator performed best among candidate estimators that were not omnisciently correct. In one setting, the augmented IPW estimator reduced the standard error by nearly 30%, compared to a standard Horvitz-Thompson IPW estimator; such a standard error reduction is equivalent to doubling the sample size. These results highlight the gains and losses that may be incurred when model assumptions are made in any analysis.