The paper presents a (partially informal) discussion of various bootstrap methods designed for the statistical analysis of data with possibly missing values: the nonparametric bootstrap, the full mechanism and the multiple imputation bootstrap. The first utilizes resampling from the available (incomplete) data. The full mechanism requires knowledge of the concealment mechanism transforming the original data \({\mathbf x}\) into the observations \({\mathbf o}\), while for the multiple imputation bootstrap one needs, in a Bayesian framework, knowledge of the conditional densities \(f({\mathbf x}|{\mathbf o})\).
In his comment, D. Rubin comes to the conclusion that “Efron can be read as implying that confidence intervals based on the nonparametric bootstrap are valid whether or not the imputation method tracks the actual mechanism that created the missing data”. This reviewer also has the impression that some further clarifying remarks would have been worthwhile, namely that the validity of each choice of a bootstrap heavily depends on having specified the correct model.