Open Access
January, 1989 Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates
M. Falk, R.-D. Reiss
Ann. Probab. 17(1): 362-371 (January, 1989). DOI: 10.1214/aop/1176991515


Under fairly general assumptions on the underlying distribution function, the bootstrap process, pertaining to the sample $q$-quantile, converges weakly in $D_\mathbb{R}$ to the standard Brownian motion. Furthermore, weak convergence of a smoothed bootstrap quantile estimate is proved which entails that in this particular case the smoothed bootstrap estimate outperforms the nonsmoothed one.


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M. Falk. R.-D. Reiss. "Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates." Ann. Probab. 17 (1) 362 - 371, January, 1989.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0684.62036
MathSciNet: MR972792
Digital Object Identifier: 10.1214/aop/1176991515

Primary: 62G30
Secondary: 60F05 , 60G99

Keywords: bootstrap process , Brownian motion , Empirical distribution function , kernel estimate , Sample quantile

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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