BOOTSTRAPPING GENERALIZED U-PROCESSES AND V-PROCESSES AND THEIR APPLICATIONS IN PROJECTION PURSUIT

摘要

In this paper, we study bootstrap approximation for generalized U-processes (GUP) indexed by a class of functions. Under mild conditions we obtain that the asymptotic distributions of bootstrapping generalized U-processes (BGUP) are the same as those of GUP almost surely. As a result, the asymptotic properties of bootstrap approximation for PP generalized U-processes (BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalized V-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUP and GVP.