BAYESIAN BOOTSTRAPS FOR U-PROCESSES, HYPOTHESIS TESTS AND CONVERGENCE OF DIRICHLET U-PROCESSES
Dixin Zhang · 2001
Abstract: Suppose F is a class of bounded or unbounded functions. We construct a Bayesian bootstrapped U-process over F and study the limiting behavior of the process. We obtain conditional central limit theorems for Bayesian bootstrapped U-processes and Dirichlet U-processes over F, and discuss Bayesian bootstrap ap-proximations 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