H. Ishwaran - The Cleveland Clinic Foundation. Postal Address; Depatrment of Biostatistics and Epidemiology, ۹۵۰۰ Euclid Avenue Cleveland, OH ۴۴۱۹۵, U.S.A.
Lanclot - The Cleveland Clinic Foundation. Postal Address; Depatrment of Biostatistics and Epidemiology, ۹۵۰۰ Euclid Avenue Cleveland, OH ۴۴۱۹۵, U.S.A.
F. James - Department of mathernatical Sciences, The Johns Hopkins University, ۳۴th & Cahrles Streets, Baltimore, MD ۲۱۲۱۸, U.S.A
M. Zarepour - Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, KIN ۶N۵, Canada.

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.

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