| Abstract: | The bootstrap and smoothed bootstrap have been shown to be a very powerful tool in statistics and its applications. In this paper, we develop the technique of rescaling in the smoothed bootstrap, extending Silverman and Young's (1987) 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, and therefore outperforms the existing methods. The new method is investigated in the problems of estimation of global and local functionals and kernel density estimation. |
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