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Statistica Sinica 11(2001), 463-478



BAYESIAN BOOTSTRAPS FOR U-PROCESSES,

HYPOTHESIS TESTS AND CONVERGENCE OF

DIRICHLET U-PROCESSES


Dixin Zhang


Guangdong Commercial College


Abstract: Suppose ${\cal F}$ is a class of bounded or unbounded functions. We construct a Bayesian bootstrapped U-process over ${\cal F}$ and study the limiting behavior of the process. We obtain conditional central limit theorems for Bayesian bootstrapped U-processes and Dirichlet U-processes over ${\cal F}$, 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.



Key words and phrases: Bayesian bootstrap approximation, conditional central limit theorem, U-process.



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