The cluster bootstrap consistency in generalized estimating equations

The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference.