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Optimizing the smoothed bootstrap

  • Suojin Wang
Estimation And Prediction

Abstract

In this paper we develop the technique of a generalized rescaling in the smoothed bootstrap, extending Silverman and Young's idea of shrinking. Unlike most existing methods of smoothing, with a proper choice of the rescaling parameter the rescaled smoothed bootstrap method produces estimators that have the asymptotic minimum mean (integrated) squared error, asymptotically improving existing bootstrap methods, both smoothed and unsmoothed. In fact, the new method includes existing smoothed bootstrap methods as special cases. This unified approach is investigated in the problems of estimation of global and local functionals and kernel density estimation. The emphasis of this investigation is on theoretical improvements which in some cases offer practical potential.

Key words and phrases

Bootstrap functional estimation kernel density estimation mean integrated squared error mean squared error quantile rescaling smoothing 

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Copyright information

© The Institute of Statistical Mathematics 1995

Authors and Affiliations

  • Suojin Wang
    • 1
  1. 1.Department of StatisticsTexas A&M UniversityCollege StationU.S.A.

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