Perturbing the minimand resampling with Gamma(1,1) random variables as an extension of the Bayesian Bootstrap

Jin et al. (2001) proposed a clever resampling method useful for calculating a variance estimate of the solution to an estimating equation. The method multiplies each independent subject's contribution to the estimating equation by a randomly sampled random variable with mean and variance 1. They showed that this resampling technique gives consistent variance estimates under mild conditions. Rubin (1981. The Bayesian Bootstrap. Ann. Statist. 9, 130-134) proposed the Bayesian Bootstrap as a modification of the usual bootstrap. In this note, we show that the Bayesian Bootstrap is a special case of Jin et al.'s resampling approach.