Bootstrapping generalizedU-processes andV-processes and their applications in projection pursuit

In this paper, we study bootstrap approximation for generalizedU-processes (GUP) indexed by a class of functions. Under mild conditions we obtain that the asymptotic distributions of bootstrapping generalizedU-processes (BGUP) are the same as those of GUP almost surely. As a result, the asymptotic properties of bootstrap approximation for PP generalizedU-processes (BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUP and GVP.This project is supported by the National Natural Science Foundation of China and the Science Foundation of Educational Committee of Guizhou.