Acta Mathematicae Applicatae Sinica

, Volume 12, Issue 4, pp 354–362 | Cite as

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

  • Zhang Dixin 
  • Li Guoying 
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Abstract

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.

Key words

Bootstrap projection pursuit (PP) U-processes asymptotic distribution 
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Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1996

Authors and Affiliations

  • Zhang Dixin 
    • 1
  • Li Guoying 
    • 2
  1. 1.Department of StatisticsGuizhou College of Finance and EconomicsGuiyangChina
  2. 2.Institute of Systems Sciencethe Chinese Academy of SciencesBeijingChina

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