On a Second-Order Asymptotic Property of the Bayesian Bootstrap Mean

Abstract

It is shown that the Bayesian bootstrapapproximation to the posterior distribution of theunknown mean (with respect to a Dirichlet processprior) is more accurate than both the standardnormal approximation and the bootstrapapproximation. It is also shown that the Bayesianbootstrap approximation to the samplingdistribution of the sample average is not asaccurate as the bootstrap approximation.