Bayesian bootstraps for U-processes, hypothesis tests and convergence of dirichlet U-processes

Suppose F is a class of bounded err unbounded functions. We construct a Bayesian bootstrapped U-process over F and study the limiting behavior of the process. W:e obtain conditional central limit theorems for Bayesian bootstrapped U-processes and Dirichlet U-processes over F, and discuss Bayesian bootstrap approximations for U-processes, Some problems concerning hypothesis testing in high-dimensional spaces are solved by combining the results in this paper with the Projection Pursuit method.