Abstract: Suppose is a class of bounded or unbounded functions. We construct a Bayesian bootstrapped U-process over and study the limiting behavior of the process. We obtain conditional central limit theorems for Bayesian bootstrapped U-processes and Dirichlet U-processes over , 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.
Key words and phrases: Bayesian bootstrap approximation, conditional central limit theorem, U-process.