The Annals of Probability

Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates

M. Falk and R.-D. Reiss

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Abstract

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.

Article information

Source
Ann. Probab. Volume 17, Number 1 (1989), 362-371.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176991515

Digital Object Identifier
doi:10.1214/aop/1176991515

Mathematical Reviews number (MathSciNet)
MR972792

Zentralblatt MATH identifier
0684.62036

JSTOR
links.jstor.org

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 60F05: Central limit and other weak theorems 60G99: None of the above, but in this section

Keywords
Sample quantile empirical distribution function bootstrap process Brownian motion kernel estimate

Citation

Falk, M.; Reiss, R.-D. Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates. Ann. Probab. 17 (1989), no. 1, 362--371. doi:10.1214/aop/1176991515. http://projecteuclid.org/euclid.aop/1176991515.


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