On Development of the Weighted Bootstrap

It is a well known fact that the Efron’s usual bootstrap fails for the mean of heavy tail distributions. We demonstrate that this same type of failure also occurs in many types of weighted bootstraps, including the Bayesian bootstrap. Only through a careful selection for the weights we can produce a consistent weighted bootstrap procedure that will work for the mean and other useful statistics.

Keywords:

Bayesian Bootstrap , heavy tail distribution , point process , Dirichlet process.